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  • A characterization of one‐component inner functions
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-27
    Artur Nicolau; Atte Reijonen

    We present a characterization of one‐component inner functions in terms of the location of their zeros and their associated singular measure. As consequence we answer several questions posed by Cima and Mortini. In particular, we prove that for any inner function Θ whose singular set has measure zero, one can find a Blaschke product B such that B Θ is one‐component. We also obtain a characterization

    更新日期:2020-07-27
  • The contact structure induced by a line fibration of R3 is standard
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-27
    Tilman Becker; Hansjörg Geiges

    Building on the work of and answering a question by Michael Harrison, we show that any contact structure on R 3 induced by a line fibration of R 3 is diffeomorphic to the standard contact structure.

    更新日期:2020-07-27
  • An enhanced uncertainty principle for the Vaserstein distance
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-27
    Tom Carroll; Xavier Massaneda; Joaquim Ortega‐Cerdà

    We improve some recent results of Sagiv and Steinerberger that quantify the following uncertainty principle: for a function f with mean zero, then either the size of the zero set of the function or the cost of transporting the mass of the positive part of f to its negative part must be big. We also provide a sharp upper estimate of the transport cost of the positive part of an eigenfunction of the

    更新日期:2020-07-27
  • Explicit degree bounds for right factors of linear differential operators
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-27
    Alin Bostan; Tanguy Rivoal; Bruno Salvy

    If a linear differential operator with rational function coefficients is reducible, its factors may have coefficients with numerators and denominators of very high degrees. When the base field is C , we give a completely explicit bound for the degrees of the monic right factors in terms of the degree and the order of the original operator, as well as of the largest modulus of the local exponents at

    更新日期:2020-07-27
  • Chebotarev links are stably generic
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-21
    Jun Ueki

    We discuss the relationship between two analogues in a 3‐manifold of the set of prime ideals in a number field. We prove that if ( K i ) i ∈ N > 0 is a sequence of knots obeying the Chebotarev law in the sense of Mazur and McMullen, then K = ∪ i K i is a stably generic link in the sense of Mihara. An example we investigate is the planetary link of a fibered hyperbolic finite link in S 3 . We also observe

    更新日期:2020-07-21
  • A renewal theorem for relatively stable variables
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-21
    Kôhei Uchiyama

    Let F { d x } be a relatively stable (r.s.) probability distribution on the whole real line and S n the random walk started at the origin with step distribution F . We obtain an exact asymptotic form of the Green measure U { x + d y } = ∑ n = 0 ∞ P [ S n − x ∈ d y ] as x → ∞ when S n is transient and S n → ∞ in probability. If F is concentrated on [ 0 , ∞ ) , it is r.s. if and only if ℓ ( x ) : = ∫

    更新日期:2020-07-21
  • A note on band surgery and the signature of a knot
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-21
    Allison H. Moore; Mariel Vazquez

    Band surgery is an operation relating pairs of knots or links in the three‐sphere. We prove that if two quasi‐alternating knots K and K ′ of the same square‐free determinant are related by a band surgery, then the absolute value of the difference in their signatures is either 0 or 8. This obstruction follows from a more general theorem about the difference in the Heegaard Floer d ‐invariants for pairs

    更新日期:2020-07-21
  • Actions of homeomorphism groups of manifolds admitting a nontrivial finite free action
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-20
    Lei Chen

    In this paper, we study the action of Homeo 0 ( M ) , the identity component of the group of homeomorphisms of an n ‐dimensional manifold M with an F p ‐free action, on another manifold N of dimension n + k < 2 n . We prove that if M is not an F p ‐homology sphere, then N ≅ M × K for a homology manifold K such that the action of Homeo 0 ( M ) on M is natural and on K is trivial. We also prove that

    更新日期:2020-07-20
  • Test vectors for non‐Archimedean Godement–Jacquet zeta integrals
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-18
    Peter Humphries

    Given an induced representation of Langlands type ( π , V π ) of GL n ( F ) with F non‐Archimedean, we show that there exist explicit choices of matrix coefficient β and Schwartz–Bruhat function Φ for which the Godement–Jacquet zeta integral Z ( s , β , Φ ) attains the L ‐function L ( s , π ) .

    更新日期:2020-07-18
  • Monochromatic equilateral triangles in the unit distance graph
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-16
    Eric Naslund

    Let χ Δ ( R n ) denote the minimum number of colors needed to color R n so that there will not be a monochromatic equilateral triangle with side length 1. Using the slice rank method, we reprove a result of Frankl and Rodl, and show that χ Δ ( R n ) grows exponentially with n . This technique substantially improves upon the best known quantitative lower bounds for χ Δ ( R n ) , and we obtain χ Δ R

    更新日期:2020-07-16
  • Heisenberg uniqueness pairs for the hyperbola
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-16
    Deb Kumar Giri; Rama Rawat

    Let Γ be the hyperbola { ( x , y ) ∈ R 2 : x y = 1 } and Λ β be the lattice‐cross defined by Λ β = ( Z × { 0 } ) ∪ ( { 0 } × β Z ) in R 2 , where β is a positive real. A result of Hedenmalm and Montes‐Rodríguez says that ( Γ , Λ β ) is a Heisenberg uniqueness pair if and only if β ⩽ 1 . In this paper, we show that for a rational perturbation of Λ β , namely Λ β θ = ( Z + { θ } ) × { 0 } ∪ { 0 } × β

    更新日期:2020-07-16
  • Schwarz‐type lemmas for generalized holomorphic maps between pseudo‐Hermitian manifolds and Hermitian manifolds
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-16
    Tian Chong; Yuxin Dong; Yibin Ren; Weike Yu

    In this paper, we consider some generalized holomorphic maps between pseudo‐Hermitian manifolds and Hermitian manifolds. By Bochner formulas and comparison theorems, we establish related Schwarz‐type results. As corollaries, the Liouville theorem and little Picard theorem for basic CR functions are deduced. Finally, we study CR Carathéodory pseudo‐distance on CR manifolds.

    更新日期:2020-07-16
  • Varieties of monoids with complex lattices of subvarieties
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-15
    Sergey V. Gusev; Edmond W. H. Lee

    A variety is finitely universal if its lattice of subvarieties contains an isomorphic copy of every finite lattice. Examples of finitely universal varieties of semigroups have been available since the early 1970s, but it is unknown if there exists a finitely universal variety of monoids. The main objective of the present article is to exhibit the first examples of finitely universal varieties of monoids

    更新日期:2020-07-15
  • Brauer–Manin obstruction for Erdős–Straus surfaces
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-07
    Martin Bright; Daniel Loughran

    We study the failure of the integral Hasse principle and strong approximation for the Erdős–Straus conjecture using the Brauer–Manin obstruction.

    更新日期:2020-07-07
  • Pfister's local–global principle and systems of quadratic forms
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-07-02
    Uriya A. First

    Let q be a unimodular quadratic form over a field K . Pfister's famous local–global principle asserts that q represents a torsion class in the Witt group of K if and only if it has signature 0, and that in this case, the order of Witt class of q is a power of 2. We give two analogues of this result to systems of quadratic forms, the second of which applying only to nonsingular pairs. We also prove

    更新日期:2020-07-02
  • On a conjecture of Gowers and Long
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-30
    Ben Green

    We show that rounding to a δ ‐net in SO ( 3 ) is not close to a group operation, thus confirming a conjecture of Gowers and Long.

    更新日期:2020-07-01
  • Famille admise associée à une valuation de K(X)
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-30
    Michel Vaquié

    Let K be a field equipped with a valuation ν and let L = K ( x ) be a transcendental extension of K . Every valuation μ of L which extends ν is determined by its restriction to the polynomial ring K [ x ] . We know how to associate to this valuation μ a family of valuations A = ( μ i ) i ∈ I of K [ x ] , called the associated admitted family that converges in a certain sense towards the valuation μ

    更新日期:2020-07-01
  • The Erdős–Ulam problem, Lang's conjecture and uniformity
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-29
    Kenneth Ascher; Lucas Braune; Amos Turchet

    A rational distance set is a subset of the plane such that the distance between any two points is a rational number. We show, assuming Lang's conjecture, that the cardinalities of rational distance sets in general position are uniformly bounded, generalizing results of Solymosi–de Zeeuw, Makhul–Shaffaf, Shaffaf and Tao. In the process, we give a criterion for certain varieties with non‐canonical singularities

    更新日期:2020-06-30
  • Variations on a theme of Hardy concerning the maximum modulus
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-29
    Leticia Pardo‐Simón; David J. Sixsmith

    In 1909, Hardy gave an example of a transcendental entire function, f , with the property that the set of points where f achieves its maximum modulus, M ( f ) , has infinitely many discontinuities. This is one of only two known examples of such an entire function.

    更新日期:2020-06-29
  • An aperiodic monotile that forces nonperiodicity through dendrites
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-28
    Michael Mampusti; Michael F. Whittaker

    We introduce a new type of aperiodic hexagonal monotile; a prototile that admits infinitely many tilings of the plane, but any such tiling lacks any translational symmetry. Adding a copy of our monotile to a patch of tiles must satisfy two rules that apply only to adjacent tiles. The first is inspired by the Socolar–Taylor monotile, but can be realised by shape alone. The second is a dendrite rule;

    更新日期:2020-06-29
  • Connes' bicentralizer problem for q‐deformed Araki–Woods algebras
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-28
    Cyril Houdayer; Yusuke Isono

    Let ( H R , U t ) be any strongly continuous orthogonal representation of R on a real (separable) Hilbert space H R . For any q ∈ ( − 1 , 1 ) , we denote by Γ q ( H R , U t ) ′ ′ the q ‐deformed Araki–Woods algebra introduced by Shlyakhtenko and Hiai. In this paper, we prove that Γ q ( H R , U t ) ′ ′ has trivial bicentralizer if it is a type III 1 factor. In particular, we obtain that Γ q ( H R ,

    更新日期:2020-06-29
  • Laminations of a graph on a pair of pants
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-28
    Sanjay Ramassamy

    A lamination of a graph embedded on a surface is a collection of pairwise disjoint non‐contractible simple closed curves drawn on the graph. In the case when the surface is a sphere with three punctures (a.k.a. a pair of pants), we first identify the lamination space of a graph embedded on that surface as a lattice polytope, then we characterize the polytopes that arise as the lamination space of some

    更新日期:2020-06-29
  • On the failure of the first Čech homotopy group to register geometrically relevant fundamental group elements
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-28
    Jeremy Brazas; Hanspeter Fischer

    We construct a space P for which the canonical homomorphism π 1 ( P , p ) → π ̌ 1 ( P , p ) from the fundamental group to the first Čech homotopy group is not injective, although it has all of the following properties: (1) P ∖ { p } is a 2‐manifold with connected non‐compact boundary; (2) P is connected and locally path connected; (3) P is strongly homotopically Hausdorff; (4) P is homotopically path

    更新日期:2020-06-29
  • Singularities and radical initial ideals
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-28
    Alexandru Constantinescu; Emanuela De Negri; Matteo Varbaro

    What kind of reduced monomial schemes can be obtained as a Gröbner degeneration of a smooth projective variety? Our conjectured answer is: only Stanley–Reisner schemes associated to acyclic Cohen–Macaulay simplicial complexes. This would imply, in particular, that only curves of genus zero have such a degeneration. We prove this conjecture for degrevlex orders, for elliptic curves over totally real

    更新日期:2020-06-29
  • Derivatives of normal Jacobi operator on real hypersurfaces in the complex quadric
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-25
    Hyunjin Lee; Juan de Dios Pérez; Young Jin Suh

    Suh (Math. Nachr . 290 (2017) 442–451) proved that there are no Hopf real hypersurfaces in the complex quadric that have parallel normal Jacobi operators. Motivated by this result, in this paper, we introduce the notions of C ‐parallel and Reeb parallel for normal Jacobi operators, which generalize the notion ‘parallel’. First we obtain a non‐existence theorem of Hopf real hypersurfaces with C ‐parallel

    更新日期:2020-06-25
  • Irreducible nonsurjective endomorphisms of Fn are hyperbolic
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-25
    Jean Pierre Mutanguha

    Previously, Reynolds showed that any irreducible nonsurjective endomorphism can be represented by an irreducible immersion on a finite graph. We give a new proof of this and also show a partial converse holds when the immersion has connected Whitehead graphs with no cut vertices. The next result is a characterization of finitely generated subgroups of the free group that are invariant under an irreducible

    更新日期:2020-06-25
  • On the heat content for the Poisson kernel over the unit ball in the euclidean space
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-24
    Luis Acuña Valverde

    This paper studies, by employing analytical tools, the small‐time behavior of the heat content for the Poisson kernel over the unit ball in R d , d ⩾ 2 by working with its related set covariance function. As a result, we obtain a representation for the third term in the expansion of the heat content over the unit ball and provide the explicit form of this term in the particular cases d = 2 and d =

    更新日期:2020-06-24
  • Erratum: Moment curves and cyclic symmetry for positive Grassmannians
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-23
    Steven N. Karp

    Due to a typesetting error, one equation and two pieces of line art were omitted from this article 1 when it was originally published. In the introduction, the following image of a regular unit octagon inscribed in a unit circle was missing at the end of page 901: Furthermore, the missing equation 4.6 on page 913 of the article should correctly appear as follows: (4.6) The missing content has been

    更新日期:2020-06-24
  • Quasitriangular coideal subalgebras of Uq(g) in terms of generalized Satake diagrams
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-23
    Vidas Regelskis; Bart Vlaar

    Let g be a finite‐dimensional semisimple complex Lie algebra and θ an involutive automorphism of g . According to Letzter, Kolb and Balagović the fixed‐point subalgebra k = g θ has a quantum counterpart B , a coideal subalgebra of the Drinfeld–Jimbo quantum group U q ( g ) possessing a universal K ‐matrix K . The objects θ , k , B and K can all be described in terms of Satake diagrams. In the present

    更新日期:2020-06-23
  • Linear recurrence sequences and the duality defect conjecture
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-23
    Grayson Jorgenson

    It is conjectured that the dual variety of a smooth nonlinear variety X ⊆ P N of dimension dim ( X ) > 2 N 3 is a hypersurface, an expectation known as the duality defect conjecture. This would follow from the truth of Hartshorne's complete intersection conjecture but nevertheless remains open for the case of subvarieties of codimension > 2 . A combinatorial approach to prove the conjecture in the

    更新日期:2020-06-23
  • The analytic class number formula for 1‐dimensional affine schemes
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-22
    Bruce W. Jordan; Bjorn Poonen

    We derive an analytic class number formula valid for an order in a product of S ‐integers in global fields, or equivalently for reduced finite‐type affine schemes of pure dimension 1 over Z .

    更新日期:2020-06-22
  • A local version of the Myers–Steenrod theorem
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-22
    Francesco Pediconi

    We prove the Myers–Steenrod theorem for local topological groups of isometries acting on pointed C k , α ‐Riemannian manifolds, with k + α > 0 . As an application, we infer a new regularity result for a certain class of locally homogeneous Riemannian metrics.

    更新日期:2020-06-22
  • A note on stochastic dominance, uniform integrability and lattice properties
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-22
    Max Nendel

    In this work, we discuss completeness for the lattice orders of first and second order stochastic dominance. The main results state that both first‐ and second‐order stochastic dominance induce Dedekind super complete lattices, that is, lattices in which every bounded nonempty subset has a countable subset with identical least upper bound and greatest lower bound. Moreover, we show that, if a suitably

    更新日期:2020-06-22
  • A note on the maximum of the Riemann zeta function on the 1‐line
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-22
    Winston Heap

    We investigate the relationship between the maximum of the zeta function on the 1‐line and the maximal order of S ( t ) , the error term in the number of zeros up to height t . We show that the conjectured upper bounds on S ( t ) along with the Riemann hypothesis imply a conjecture of Littlewood that max t ∈ [ 1 , T ] | ζ ( 1 + i t ) | ∼ e γ log log T . The relationship in the region 1 / 2 < σ < 1

    更新日期:2020-06-22
  • Liftable derived equivalences and objective categories
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-22
    Xiaofa Chen; Xiao‐Wu Chen

    We give two proofs of the following theorem and a partial generalization: if a finite‐dimensional algebra A is derived equivalent to a smooth projective scheme, then any derived equivalence between A and another algebra B is standard, that is, isomorphic to the derived tensor functor by a two‐sided tilting complex. The main ingredients of the proofs are as follows: (1) between the derived categories

    更新日期:2020-06-22
  • Haar null and Haar meager sets: a survey and new results
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-21
    Márton Elekes; Donát Nagy

    We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the techniques that may enable the reader to prove results in this area. We also present several recently introduced ideas, including the notion of Haar meager sets, which

    更新日期:2020-06-22
  • A note on the Brauer group and the Brauer–Manin set of a product
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-21
    Chang Lv

    We generalize the results of Skorobogatov and Zarhin considering the commutativity of Brauer groups (and Brauer–Manin sets) with taking product of two varieties, by relaxing the condition that varieties are projective.

    更新日期:2020-06-22
  • 2‐adic slopes of Hilbert modular forms over Q(5)
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-21
    Christopher Birkbeck

    We show that for arithmetic weights with a fixed finite‐order character, the slopes of U p for p = 2 (which is inert) acting on overconvergent Hilbert modular forms of level U 0 ( 4 ) are independent of the (algebraic part of the) weight and can be obtained by a simple recipe from the classical slopes in parallel weight 3.

    更新日期:2020-06-22
  • On the generalized Fitting height and insoluble length of finite groups
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-15
    Robert M. Guralnick; Gareth Tracey

    We prove two conjectures of E. Khukhro and P. Shumyatsky concerning the Fitting height and insoluble length of finite groups. As a by‐product of our methods, we also prove a generalization of a result of Flavell, which itself generalizes Wielandt's Zipper Lemma and provides a characterization of subgroups contained in a unique maximal subgroup. We also derive a number of consequences of our theorems

    更新日期:2020-06-15
  • Torsion points with multiplicatively dependent coordinates on elliptic curves
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-15
    Fabrizio Barroero; Min Sha

    In this paper, we study the finiteness problem of torsion points on an elliptic curve whose coordinates satisfy some multiplicative dependence relations. In particular, we prove that on an elliptic curve defined over a number field there are only finitely many torsion points whose coordinates are multiplicatively dependent. Moreover, we produce an effective result when the elliptic curve is defined

    更新日期:2020-06-15
  • Disproportionate division
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-13
    Logan Crew; Bhargav Narayanan; Sophie Spirkl

    We study the disproportionate version of the classical cake‐cutting problem: how efficiently can we divide a cake, here [0,1], among n ⩾ 2 agents with different demands α 1 , α 2 , ⋯ , α n summing to 1? When all the agents have equal demands of α 1 = α 2 = ⋯ = α n = 1 / n , it is well known that there exists a fair division with n − 1 cuts, and this is optimal. For arbitrary demands on the other hand

    更新日期:2020-06-13
  • Weak‐type estimates for the Bergman projection on the polydisc and the Hartogs triangle
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-13
    Zhenghui Huo; Brett D. Wick

    In this paper, we investigate the weak‐type regularity of the Bergman projection. The two domains we focus on are the polydisc and the Hartogs triangle. For the polydisc, we provide a proof that the weak‐type behavior is of ‘ L log L ’ type. This result is likely known to the experts, but does not appear to be in the literature. For the Hartogs triangle, we show that the operator is of weak‐type (4

    更新日期:2020-06-13
  • Just infiniteness of the generalized Nottingham group
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-13
    Davide Veronelli

    The Nottingham group is the unique Sylow pro‐ p subgroup of the automorphism group of the formal power series algebra over a finite field. This group has been intensively studied in the last decades for its interesting properties, just infiniteness being one of the most remarkable. Shalev and Leedham‐Green introduced the generalized Nottingham groups and confirmed that they are just infinite, however

    更新日期:2020-06-13
  • Infinite 32‐generated groups
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-10
    Casey Donoven; Scott Harper

    Every finite simple group can be generated by two elements, and Guralnick and Kantor proved that, moreover, every nontrivial element is contained in a generating pair. Groups with this property are said to be 3 2 ‐generated. Thompson's group V was the first finitely presented infinite simple group to be discovered. The Higman–Thompson groups V n and the Brin–Thompson groups m V are two families of

    更新日期:2020-06-10
  • Idempotent characters and equivariantly multiplicative splittings of K‐theory
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-09
    Benjamin Böhme

    We classify the primitive idempotents of the p ‐local complex representation ring of a finite group G in terms of the cyclic subgroups of order prime to p and show that they all come from idempotents of the Burnside ring. Our results hold without adjoining roots of unity or inverting the order of G , thus extending classical structure theorems. We then derive explicit group‐theoretic obstructions for

    更新日期:2020-06-09
  • Traces of reciprocal singular moduli
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-09
    Claudia Alfes‐Neumann; Markus Schwagenscheidt

    We show that the generating series of traces of reciprocal singular moduli is a mixed mock modular form of weight 3 / 2 whose shadow is given by a linear combination of products of unary and binary theta functions. To prove these results, we extend the Kudla–Millson theta lift of Bruinier and Funke to meromorphic modular functions.

    更新日期:2020-06-09
  • A Riemann–Kempf singularity theorem for higher rank Brill–Noether loci
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-09
    George H. Hitching

    Given a vector bundle V of rank r over a curve X , we define and study a surjective rational map Hilb d ( P V ) ⤍ Quot 0 , d ( V ∗ ) generalising the natural map Sym d X → Quot 0 , d ( O X ) . We then give a generalisation of the geometric Riemann–Roch theorem to vector bundles of higher rank over X . We use this to give a geometric description of the tangent cone to the higher rank Brill–Noether locus

    更新日期:2020-06-09
  • On the uniform Roe algebra as a Banach algebra and embeddings of ℓp uniform Roe algebras
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-06-09
    Bruno M. Braga; Alessandro Vignati

    We work on ℓ p uniform Roe algebras associated to metric spaces, and on their mutual embedding. We generalize results of Farah and the authors to mutual embeddings of uniform Roe algebras of operators on ℓ p spaces. Simultaneously, we obtain rigidity results for the classic uniform Roe C ∗ ‐algebras which depend only on their Banach algebra structure.

    更新日期:2020-06-09
  • Normal states are determined by their facial distances
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-05-22
    Anthony To‐Ming Lau; Chi‐Keung Ng; Ngai‐Ching Wong

    Let M be a semi‐finite von Neumann algebra with normal state space S ( M ) . For any ϕ ∈ S ( M ) , let M ϕ : = { x ∈ M : x ϕ = ϕ x } be the centralizer of ϕ with center Z ( M ϕ ) . We show that for ϕ , ψ ∈ S ( M ) , the following are equivalent. ϕ = ψ . Z ( M ψ ) ⊆ Z ( M ϕ ) and ϕ | Z ( M ϕ ) = ψ | Z ( M ϕ ) . ϕ , ψ have the same distances to all the closed faces of S ( M ) .

    更新日期:2020-05-22
  • Dorronsoro's theorem in Heisenberg groups
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-05-22
    Katrin Fässler; Tuomas Orponen

    A theorem of Dorronsoro from the 1980s quantifies the fact that real‐valued Sobolev functions on Euclidean spaces can be approximated by affine functions almost everywhere, and at all sufficiently small scales. We prove a variant of Dorronsoro's theorem in Heisenberg groups: functions in horizontal Sobolev spaces can be approximated by affine functions which are independent of the last variable. As

    更新日期:2020-05-22
  • A generalization of a theorem of Rodgers and Saxl for simple groups of bounded rank
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-05-21
    N. Gill; L. Pyber; E. Szabó

    We prove that if G is a finite simple group of Lie type and S 1 , ⋯ , S k are subsets of G satisfying ∏ i = 1 k | S i | ⩾ | G | c for some c depending only on the rank of G , then there exist elements g 1 , ⋯ , g k such that G = ( S 1 ) g 1 ⋯ ( S k ) g k . This theorem generalizes an earlier theorem of the authors and Short.

    更新日期:2020-05-21
  • Uniqueness for contagious McKean–Vlasov systems in the weak feedback regime
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-05-21
    Sean Ledger; Andreas Søjmark

    We present a simple uniqueness argument for a collection of McKean–Vlasov problems that have seen recent interest. Our first result shows that, in the weak feedback regime, there is global uniqueness for a very general class of random drivers. By weak feedback we mean the case where the contagion parameters are small enough to prevent blow‐ups in solutions. Next, we specialise to a Brownian driver

    更新日期:2020-05-21
  • On a rainbow version of Dirac's theorem
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-05-19
    Felix Joos; Jaehoon Kim

    For a collection G = { G 1 , ⋯ , G s } of not necessarily distinct graphs on the same vertex set V , a graph H with vertices in V is a G ‐transversal if there exists a bijection ϕ : E ( H ) → [ s ] such that e ∈ E ( G ϕ ( e ) ) for all e ∈ E ( H ) . We prove that for | V | = s ⩾ 3 and δ ( G i ) ⩾ s / 2 for each i ∈ [ s ] , there exists a G ‐transversal that is a Hamilton cycle. This confirms a conjecture

    更新日期:2020-05-19
  • Universality of random permutations
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-05-16
    Xiaoyu He; Matthew Kwan

    It is a classical fact that for any ε > 0 , a random permutation of length n = ( 1 + ε ) k 2 / 4 typically contains an increasing subsequence of length k . As a far‐reaching generalization, Alon conjectured that a random permutation of this same length n is typically k ‐universal , meaning that it simultaneously contains every pattern of length k . He also made the simple observation that for n = O

    更新日期:2020-05-16
  • Existence and multiplicity of solutions for double‐phase Robin problems
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-05-16
    Nikolaos S. Papageorgiou; Vicenţiu D. Rădulescu; Dušan D. Repovš

    We consider a double phase Robin problem with a Carathéodory nonlinearity. When the reaction is superlinear but without satisfying the Ambrosetti–Rabinowitz condition, we prove an existence theorem. When the reaction is resonant, we prove a multiplicity theorem. Our approach is Morse theoretic, using the notion of homological local linking.

    更新日期:2020-05-16
  • Geometric description of virtual Schottky groups
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-05-15
    Ruben A. Hidalgo

    A virtual Schottky group is a Kleinian group K containing a Schottky group G as a finite index normal subgroup. These groups correspond to those groups of automorphisms of closed Riemann surfaces which can be realized at the level of their lowest uniformizations. In this paper, we provide a geometrical structural decomposition of K . When K / G is an abelian group, an explicit free product decomposition

    更新日期:2020-05-15
  • Nonexistence and multiplicity of positive solutions for an equation with degenerate nonlocal diffusion
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-05-13
    Leszek Gasiński; João R. Santos

    We study the existence, nonexistence and multiplicity of positive solutions for a general class of degenerate nonlocal problems. The nonexistence results are provided in two different situations: under monotonicity assumptions involving the nonlinearity and without monotonicity conditions. A multiplicity result of positive solutions with ordered L p ‐norms complement some recent results obtained in

    更新日期:2020-05-13
  • Untwisting 3‐strand torus knots
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-04-22
    S. Baader; I. Banfield; L. Lewark

    We prove that the signature bound for the topological 4‐genus of 3‐strand torus knots is sharp, using McCoy's twisting method. We also show that the bound is off by at most 1 for 4‐strand and 6‐strand torus knots, and improve the upper bound on the asymptotic ratio between the topological 4‐genus and the Seifert genus of torus knots from 2/3 to 14/27.

    更新日期:2020-04-22
  • The geometry of involutions in ranked groups with a ti‐subgroup
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-04-20
    Adrien Deloro; Joshua Wiscons

    We revisit the geometry of involutions in groups of finite Morley rank. The focus is on specific configurations where, as in PGL 2 ( K ) , the group has a subgroup whose conjugates generically cover the group and intersect trivially. Our main result is the subtle yet strong statement that in such configurations the conjugates of the subgroup may not cover all strongly real elements. As an application

    更新日期:2020-04-20
  • On isometric embedding ℓpm→S∞ and unique operator space structure
    Bull. Lond. Math. Soc. (IF 0.787) Pub Date : 2020-04-18
    Samya Kumar Ray

    We study existence of linear isometric embedding of ℓ p m into S ∞ , for 1 ⩽ p < ∞ , and unique operator space structure on two‐dimensional Banach spaces. For p ∈ ( 2 , ∞ ) ∪ { 1 } , we show that indeed ℓ p 2 does not embed isometrically into S ∞ . This verifies a guess of Pisier and broadly generalizes the main result of Gupta and Reza (Houston J. Math . 44 (2018) 1205–1212). We also show that S 1

    更新日期:2020-04-18
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