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Some convexity criteria for differentiable functions on the 2-Wasserstein space Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-17 Guy Parker
We show that a differentiable function on the 2-Wasserstein space is geodesically convex if and only if it is also convex along a larger class of curves which we call ‘acceleration-free’. In particular, the set of acceleration-free curves includes all generalised geodesics. We also show that geodesic convexity can be characterised through first- and second-order inequalities involving the Wasserstein
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Rigidity and vanishing theorems for submanifolds with free boundary in the unit ball Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-15 Entao Zhao, Shunjuan Cao
In this paper, we investigate the rigidity and vanishing properties of compact submanifolds with free boundary of arbitrary codimension in the unit ball. We first show that a minimal submanifold with free boundary in the unit ball satisfying a pointwise or integral curvature pinching condition on the second fundamental form is a flat equatorial disk. Then we prove a vanishing theorem for cohomology
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Generating the homology of covers of surfaces Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-14 Marco Boggi, Andrew Putman, Nick Salter
Putman and Wieland conjectured that if Σ∼→Σ$\widetilde{\Sigma }\rightarrow \Sigma$ is a finite branched cover between closed oriented surfaces of sufficiently high genus, then the orbits of all nonzero elements of H1(Σ∼;Q)$\operatorname{H}_1(\widetilde{\Sigma };\mathbb {Q})$ under the action of lifts to Σ∼$\widetilde{\Sigma }$ of mapping classes on Σ$\Sigma$ are infinite. We prove that this holds
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Most likely balls in Banach spaces: Existence and nonexistence Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-11 Bernd Schmidt
We establish a general criterion for the existence of convex sets of fixed shape as, for example, balls of a given radius, of maximal probability on Banach spaces. We also provide counterexamples, showing that their existence may fail even in some common situations.
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Degrees of the stretched Kostka quasi-polynomials Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-13 Shiliang Gao, Yibo Gao
We provide a type-uniform formula for the degree of the stretched Kostka quasi-polynomial Kλ,μ(N)$K_{\lambda,\mu }(N)$ in all classical types, improving a previous result by McAllister in slr(C)$\mathfrak {sl}_r(\mathbb {C})$. Our proof relies on a combinatorial model for the weight multiplicity by Berenstein and Zelevinsky.
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Weak approximation of symmetric products and norm varieties Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-13 Sheng Chen, Ziyang Zhang
Let k$k$ be a number field. For a variety X$X$ over k$k$ that satisfies weak approximation with Brauer–Manin obstruction, we study the same property for smooth projective models of its symmetric products. Based on the same method, we also explore the property of weak approximation with Brauer–Manin obstruction for norm varieties.
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Almost spanning distance trees in subsets of finite vector spaces Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-08 Debsoumya Chakraborti, Ben Lund
For d⩾2$d\geqslant 2$ and an odd prime power q$q$, consider the vector space Fqd$\mathbb {F}_q^d$ over the finite field Fq$\mathbb {F}_q$, where the distance between two points (x1,…,xd)$(x_1,\ldots ,x_d)$ and (y1,…,yd)$(y_1,\ldots ,y_d)$ is defined as ∑i=1d(xi−yi)2$\sum _{i=1}^d (x_i-y_i)^2$. A distance graph is a graph associated with a nonzero distance to each of its edges. We show that large subsets
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Upper bounds for Heilbronn's triangle problem in higher dimensions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-07 Dmitrii Zakharov
We develop a new simple approach to prove upper bounds for generalizations of the Heilbronn's triangle problem in higher dimensions. Among other things, we show the following: for fixed d⩾1$d \geqslant 1$, any subset of [0,1]d$[0, 1]^d$ of size n$n$ contains
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A shorter note on shorter pants Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-07 Hugo Parlier
This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best-known bound for closed surfaces.
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Long-time existence of Brownian motion on configurations of two landmarks Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-07 Karen Habermann, Philipp Harms, Stefan Sommer
We study Brownian motion on the space of distinct landmarks in Rd$\mathbb {R}^d$, considered as a homogeneous space with a Riemannian metric inherited from a right-invariant metric on the diffeomorphism group. As of yet, there is no proof of long-time existence of this process, despite its fundamental importance in statistical shape analysis, where it is used to model stochastic shape evolutions. We
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Perpetual cutoff method and discrete Ricci curvature bounds with exceptions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-05 Florentin Münch
One of the main obstacles regarding Bakry–Emery curvature on graphs is that the results require a global uniform lower curvature bounds where no exception sets are allowed. We overcome this obstacle by introducing the perpetual cutoff method. As applications, we prove gradient estimates only requiring curvature bounds on parts of the graph. Moreover, we sharply upper bound the distance to the exception
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Small codes Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-04 Igor Balla
Determining the maximum number of unit vectors in Rr$\mathbb {R}^r$ with no pairwise inner product exceeding α$\alpha$ is a fundamental problem in geometry and coding theory. In 1955, Rankin resolved this problem for all α⩽0$\alpha \leqslant 0$, and in this paper, we show that the maximum is (2+o(1))r$(2+o(1))r$ for all 0⩽α≪r−2/3$0 \leqslant \alpha \ll r^{-2/3}$, answering a question of Bukh and
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Extreme values of L-functions of newforms Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-03-03 Sanoli Gun, Rashi Lunia
In 2008, Soundararajan showed that there exists a normalized Hecke eigenform f$f$ of weight k$k$ and level one such that
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A vanishing theorem for varieties with finitely many solvable group orbits Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-28 Yiyu Wang
We reprove and generalize a result proved by Yavin that the intersection cohomology groups of a toric variety with coefficient in a nontrivial rank one local system vanish. We prove a similar vanishing result for a certain class of varieties on which a connected linear solvable group acts, including all spherical varieties.
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Localization of eigenfunctions in the Dirichlet beaker Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-28 G. Cardone, S. A. Nazarov, J. Taskinen
We construct the asymptotics of the eigenpairs of the Dirichlet problem for the Laplace operator in a thin-walled beaker and prove the localization effect for the functions near the bottom edge, a smooth closed contour, of the beaker. The main asymptotic terms are described by the eigenpairs of an ordinary differential equation on the edge and by the single eigenvalue belonging to the discrete spectrum
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Character sums over sparse elements of finite fields Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-27 László Mérai, Igor E. Shparlinski, Arne Winterhof
We estimate mixed character sums of polynomial values over elements of a finite field Fqr$\mathbb {F}_{q^r}$ with sparse representations in a fixed ordered basis over the subfield Fq$\mathbb {F}_q$. First we use a combination of the inclusion–exclusion principle with bounds on character sums over linear subspaces to get nontrivial bounds for large q$q$. Then we focus on the particular case q=2$q=2$
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Constructing Galois representations with prescribed Iwasawa λ-invariant Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-26 Anwesh Ray
Let p⩾5$p\geqslant 5$ be a prime number. We consider the Iwasawa λ$\lambda$-invariants associated to modular Bloch–Kato Selmer groups, considered over the cyclotomic Zp$\mathbb {Z}_p$-extension of Q$\mathbb {Q}$. Let g$g$ be a p$p$-ordinary cuspidal newform of weight 2 and trivial nebentype. We assume that the μ$\mu$-invariant of g$g$ vanishes, and that the image of the residual representation associated
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Exact Lagrangians in four-dimensional symplectisations Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-26 Georgios Dimitroglou Rizell
In this note, we provide explicit constructions of exact Lagrangian embeddings of tori and Klein bottles inside the symplectisation of an overtwisted contact three-manifold. Note that any closed exact Lagrangian in the symplectisation is displaceable by a Hamiltonian isotopy. We also use positive loops to exhibit elementary examples of topologically linked Legendrians that are dynamically non-interlinked
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Maximum principles and consequences for γ-translators in Rn+1 Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-23 José Torres Santaella
In this paper, we obtain several properties of translating solitons for a general class of extrinsic geometric curvature flow, where the deformation speed is given by a homogeneous smooth symmetric positive function γ$\gamma$ defined in a symmetric open cone. The main result of this paper is about the uniqueness of γ$\gamma$-translators in the class of complete graphs defined on a ball.
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Axioms for the category of Hilbert spaces and linear contractions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-24 Chris Heunen, Andre Kornell, Nesta van der Schaaf
The category of Hilbert spaces and linear contractions is characterised by elementary categorical properties that do not refer to probabilities, complex numbers, norm, continuity, convexity or dimension.
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A fake Klein bottle with bubble Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-24 W. H. Mannan
We resolve the question of the existence of a finite 2-complex with the same fundamental group and Euler characteristic as a Klein bottle with a bubble, but homotopically distinct to it.
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On Pleijel's nodal domain theorem for the Robin problem Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-21 Asma Hassannezhad, David Sher
We prove an improved Pleijel nodal domain theorem for the Robin eigenvalue problem. In particular, we remove the restriction, imposed in previous work, that the Robin parameter be non-negative. We also improve the upper bound in the statement of the Pleijel theorem. In the particular example of a Euclidean ball, we calculate the explicit value of the Pleijel constant for a generic constant Robin parameter
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On the ∞-topos semantics of homotopy type theory Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-22 Emily Riehl
Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set-based foundations. This expository article, written as lecture notes to accompany a three-part mini course delivered at the Logic and Higher Structures workshop at CIRM-Luminy, attempt to survey the state of the art, first presenting Voevodsky's simplicial model
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On quasicomplete k-surfaces in 3-dimensional space-forms Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-20 Graham Smith
In the study of immersed surfaces of constant positive extrinsic curvature in space-forms, it is natural to substitute completeness for a weaker property, which we here call quasicompleteness. We determine the global geometry of such surfaces under the hypotheses of quasicompleteness. In particular, we show that, for k>Max(0,−c)$k>\text{Max}(0,-c)$, the only quasicomplete immersed surfaces of constant
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Decay rates for the 4D energy-critical nonlinear heat equation Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-19 Leonardo Kosloff, César J. Niche, Gabriela Planas
In this paper, we address the decay of solutions to the four-dimensional energy-critical nonlinear heat equation in the critical space Ḣ1$\dot{H}^1$. Recently, it was proven that the Ḣ1$\dot{H}^1$ norm of solutions goes to zero when time goes to infinity, but no decay rates were established. By means of the Fourier Splitting Method and using properties arising from the scale invariance, we obtain
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Frieze patterns over algebraic numbers Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-17 Michael Cuntz, Thorsten Holm, Carlo Pagano
Conway and Coxeter have shown that frieze patterns over positive rational integers are in bijection with triangulations of polygons. An investigation of frieze patterns over other subsets of the complex numbers has recently been initiated by Jørgensen and the first two authors. In this paper, we first show that a ring of algebraic numbers has finitely many units if and only if it is an order in a quadratic
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Interior a priori estimates for supersolutions of fully nonlinear subelliptic equations under geometric conditions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-17 Alessandro Goffi
In this note, we prove interior a priori first- and second-order estimates for solutions of fully nonlinear degenerate elliptic inequalities structured over the vector fields of Carnot groups, under the main assumption that u$u$ is semiconvex along the fields. These estimates for supersolutions are new even for linear subelliptic inequalities in nondivergence form, whereas in the nonlinear setting
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On the effective version of Serre's open image theorem Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-17 Jacob Mayle, Tian Wang
Let E/Q$E/\mathbb {Q}$ be an elliptic curve without complex multiplication. By Serre's open image theorem, the mod ℓ$\ell$ Galois representation ρ¯E,ℓ$\overline{\rho }_{E, \ell }$ of E$E$ is surjective for each prime number ℓ$\ell$ that is sufficiently large. Under the generalized Riemann hypothesis, we give an explicit upper bound on the largest prime ℓ$\ell$, linear in the logarithm of the conductor
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On the existence of products of primes in arithmetic progressions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-13 Barnabás Szabó
We study the existence of products of primes in arithmetic progressions, building on the work of Ramaré and Walker. One of our main results is that if q$q$ is a large modulus, then any invertible residue class mod q$q$ contains a product of three primes where each prime is at most q6/5+ε$q^{6/5+\epsilon }$. Our arguments use results from a wide range of areas, such as sieve theory or additive combinatorics
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On the geometry of rod packings in the 3-torus Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-07 Connie On Yu Hui, Jessica S. Purcell
Rod packings in the 3-torus encode information of some crystal structures in crystallography. They can be viewed as links in the 3-torus, and tools from 3-manifold geometry and topology can be used to study their complements. In this paper, we initiate the use of geometrisation to study such packings. We analyse the geometric structures of the complements of simple rod packings, and find families that
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The higher regularity and decay estimates for positive solutions of fractional Choquard equations Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-06 Yinbin Deng, Xian Yang
In the paper, we study the higher regularity and decay estimates for positive solutions of the following fractional Choquard equations:
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Notes on overdetermined singular problems Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-06 Francesco Esposito, Berardino Sciunzi, Nicola Soave
We obtain some rigidity results for overdetermined boundary value problems for singular solutions in bounded domains.
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Nonautonomous double-phase equations with strong singularity and concave perturbation Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-02-05 Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Shuai Yuan
We consider a nonlinear Dirichlet problem driven by a nonautonomous double-phase differential operator and with a reaction consisting of a “strongly” singular term plus a concave perturbation. Using the Nehari method, we show the existence of a bounded strictly positive solution.
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q,t-Catalan measures Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-01-31 Ian Cavey
We introduce the q,t$q,t$-Catalan measures, a sequence of piece-wise polynomial measures on R2$\mathbb {R}^2$. These measures are defined in terms of suitable area, dinv, and bounce statistics on continuous families of paths in the plane, and have many combinatorial similarities to the q,t$q,t$-Catalan numbers. Our main result realizes the q,t$q,t$-Catalan measures as a limit of higher q,t$q,t$-Catalan
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Derived equivalences of self-injective 2-Calabi–Yau tilted algebras Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-01-05 Anders S. Kortegaard
Consider a k$k$-linear Frobenius category E$\mathcal {E}$ such that the corresponding stable category C$\mathcal {C}$ is 2-Calabi–Yau, Hom-finite with split idempotents. Let l,m∈C$l,m\in \mathcal {C}$ be maximal rigid objects with self-injective endomorphism algebras. We will show that their endomorphism algebras C(l,l)$\mathcal {C}(l,l)$ and C(m,m)$\mathcal {C}(m,m)$ are derived equivalent. Furthermore
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K-theory Soergel bimodules Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2024-01-01 Jens Niklas Eberhardt
We initiate the study of K$K$-theory Soergel bimodules, a global and K$K$-theoretic version of Soergel bimodules. We show that morphisms of K$K$-theory Soergel bimodules can be described geometrically in terms of equivariant K$K$-theoretic correspondences between Bott–Samelson varieties. We thereby obtain a natural categorification of K$K$-theory Soergel bimodules in terms of equivariant coherent sheaves
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Existence and rotatability of the two-colored Jones–Wenzl projector Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-27 Amit Hazi
The two-colored Temperley–Lieb algebra 2TLR(sn)$2\,\mathrm{TL}_R({_{s}}{n})$ is a generalization of the Temperley–Lieb algebra. The analogous two-colored Jones–Wenzl projector JWR(sn)∈2TLR(sn)$\mathrm{JW}_R({_{s}}{n}) \in 2\,\mathrm{TL}_R({_{s}}{n})$ plays an important role in the Elias–Williamson construction of the diagrammatic Hecke category. We give conditions for the existence and rotatability
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The upper bound of the harmonic mean of the Steklov eigenvalues in curved spaces Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-27 Hang Chen
Considering an n$n$-dimensional Riemannian manifold M$M$ whose sectional curvature is bounded above by κ⩽0$\kappa \leqslant 0$ and Ricci curvature is bounded below by (n−1)K$(n-1)K$, we obtain an upper bound of the harmonic mean of the first (n−1)$(n-1)$ nonzero Steklov eigenvalues for domains contained in M$M$. This can be viewed as certain isoperimetric inequality and generalizes the result on comparing
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Mather's regions of instability for annulus diffeomorphisms Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-27 Salvador Addas-Zanata, Fábio Armando Tal
Let f$f$ be a C1+ε$C^{1+\varepsilon }$ diffeomorphism of the closed annulus A$A$ that preserves orientation and the boundary components, and f∼$\widetilde{f}$ be a lift of f$f$ to its universal covering space. Assume that A$A$ is a Birkhoff region of instability for f$f$, and the rotation set of f∼$\widetilde{f}$ is a nondegenerate interval. Then there exists an open f$f$-invariant essential annulus
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Lifting problem for universal quadratic forms over totally real cubic number fields Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-26 Daejun Kim, Seok Hyeong Lee
Lifting problem for universal quadratic forms asks for totally real number fields K$K$ that admit a positive definite quadratic form with coefficients in Z$\mathbb {Z}$ that is universal over the ring of integers of K$K$. In this paper, we show K=Q(ζ7+ζ7−1)$K=\mathbb {Q}(\zeta _7+\zeta _7^{-1})$ is the only such totally real cubic field. Moreover, we show that there is no such biquadratic field.
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On the logarithmic derivative of characteristic polynomials for random unitary matrices Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-26 Fan Ge
Let U∈U(N)$U\in U(N)$ be a random unitary matrix of size N$N$, distributed with respect to the Haar measure on U(N)$U(N)$. Let P(z)=PU(z)$P(z)=P_U(z)$ be the characteristic polynomial of U$U$. We prove that for z$z$ close to the unit circle, P′P(z)$ \frac{P^{\prime }}{P}(z)$ can be approximated using zeros of P$P$ very close to z$z$, with a typically controllable error term. This is an analogue
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On Ramanujan's lost notebook and new tenth-order like identities for second-, sixth-, and eighth-order mock theta functions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-26 Eric T. Mortenson
Ramanujan's lost notebook contains many mock theta functions and mock theta function identities not mentioned in his last letter to Hardy. For example, we find the four tenth-order mock theta functions and their six identities. The six identities themselves are of a spectacular nature and were first proved by Choi. We also find eight sixth-order mock theta functions in the lost notebook, but among
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Dirichlet systems with discrete relativistic operator Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-26 Alberto Cabada, Petru Jebelean, Călin Şerban
We are concerned with Dirichlet systems involving the relativistic discrete operator
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Gâteaux or Fréchet differentiable norms on duals of interpolation spaces Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-23 Mohammad Daher
Let (B0,B1)$(B_0, B_1)$ be an interpolation couple of Banach spaces, let θ∈(0,1)$\theta \in (0, 1)$, p∈(1,+∞)$p \in (1, +\infty)$ and let (B0,B1)θ,p$(B_0, B_1)_{\theta, p}$ be the corresponding real interpolation space. We consider a norm βθ,p$\beta _{\theta, p}$ on the space (B0,B1)θ,p$(B_0, B_1)_{\theta, p}$, equivalent to the usual interpolation norm, and we show that if the norms of the dual spaces (B0)∗$
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Explicit improvements for Lp-estimates related to elliptic systems Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-23 Tim Böhnlein, Moritz Egert
We give a simple argument to obtain Lp$\mathrm{L}^p$-boundedness for heat semigroups associated to uniformly strongly elliptic systems on Rd$\mathbb {R}^d$ by using Stein interpolation between Gaussian estimates and hypercontractivity. Our results give p$p$ explicitly in terms of ellipticity. It is optimal at the endpoint p=∞$p=\infty$. We also obtain Lp$\mathrm{L}^p$-estimates for the gradient of
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Right-angled Artin groups as finite-index subgroups of their outer automorphism groups Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-23 Manuel Wiedmer
We prove that every right-angled Artin group occurs as a finite-index subgroup of the outer automorphism group of another right-angled Artin group. We furthermore show that the latter group can be chosen in such a way that the quotient is isomorphic to (Z/2Z)N$(\mathbb {Z}/2\mathbb {Z})^N$ for some N$N$. For these, we give explicit constructions using the group of pure symmetric outer automorphisms
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Extensions of polynomial plank covering theorems Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-23 Alexey Glazyrin, Roman Karasev, Alexander Polyanskii
We prove a complex polynomial plank covering theorem for not necessarily homogeneous polynomials. As the consequence of this result, we extend the complex plank theorem of Ball to the case of planks that are not necessarily centrally symmetric and not necessarily round. We also prove a weaker version of the spherical polynomial plank covering conjecture for planks of different widths.
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A note on the Hasse norm principle Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-22 Peter Koymans, Nick Rome
Let A$A$ be a finite, abelian group. We show that the density of A$A$-extensions satisfying the Hasse norm principle exists, when the extensions are ordered by discriminant. This strengthens earlier work of Frei–Loughran–Newton, who obtained a density result under the additional assumption that A/A[ℓ]$A/A[\ell]$ is cyclic with ℓ$\ell$ denoting the smallest prime divisor of #A$\# A$.
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On finite d-maximal groups Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-21 Andrea Lucchini, Luca Sabatini, Mima Stanojkovski
Let d$d$ be a positive integer. A finite group is called d$d$-maximal if it can be generated by precisely d$d$ elements, whereas its proper subgroups have smaller generating sets. For d∈{1,2}$d\in \lbrace 1,2\rbrace$, the d$d$-maximal groups have been classified up to isomorphism and only partial results have been proved for larger d$d$. In this work, we prove that a d$d$-maximal group is supersolvable
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Multivariable versions of a lemma of Kaluza's Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-20 Stefan Richter, Jesse Sautel
Let d∈N$d\in \mathbb {N}$ and f(z)=∑α∈N0dcαzα$f(z)= \sum _{\alpha \in \mathbb {N}_0^d} c_\alpha z^\alpha$ be a convergent multivariable power series in z=(z1,⋯,zd)$z=(z_1,\dots,z_d)$. In this paper, we present two conditions on the positive coefficients cα$c_\alpha$ that imply that f(z)=11−∑α∈N0dqαzα$f(z)=\frac{1}{1-\sum _{\alpha \in \mathbb {N}_0^d} q_\alpha z^\alpha}$ for nonnegative coefficients
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Quantitative rates of convergence to equilibrium for the degenerate linear Boltzmann equation on the torus Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-19 Josephine Evans, Iván Moyano
We study the linear relaxation Boltzmann equation on the torus with a spatially varying jump rate which can be zero on large sections of the domain. In Bernard and Salvarani (Arch. Ration. Mech. Anal. 208 (2013), no. 3, 977–984), Bernard and Salvarani showed that this equation converges exponentially fast to equilibrium if and only if the jump rate satisfies the geometric control condition of Bardos
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Chebyshev potentials, Fubini–Study metrics, and geometry of the space of Kähler metrics Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-19 Chenzi Jin, Yanir A. Rubinstein
The Chebyshev potential of a Hermitian metric on an ample line bundle over a projective variety, introduced by Witt Nyström, is a convex function defined on the Okounkov body. It is a generalization of the symplectic potential of a torus-invariant Kähler potential on a toric variety, introduced by Guillemin, that is a convex function on the Delzant polytope. A folklore conjecture asserts that a curve
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The continuity equation for Hermitian metrics: Calabi estimates, Chern scalar curvature, and Oeljeklaus–Toma manifolds Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-15 Shuang Liang, Xi Sisi Shen, Kevin Smith
We prove local Calabi and higher order estimates for solutions to the continuity equation introduced by La Nave–Tian and extended to Hermitian metrics by Sherman–Weinkove. We apply the estimates to show that on a compact complex manifold, the Chern scalar curvature of a solution must blow up at a finite-time singularity. Additionally, starting from certain classes of initial data on Oeljeklaus–Toma
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Embedding the prime model of real exponentiation into o-minimal exponential fields Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-15 Lothar Sebastian Krapp
Motivated by the decidability question for the theory of real exponentiation and by the Transfer Conjecture for o-minimal exponential fields, we show that, under the assumption of Schanuel's Conjecture, the prime model of real exponentiation is embeddable into any o-minimal exponential field, where the embedding is not necessarily elementary. This is a consequence of an unconditional model theoretic
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Galois actions of finitely generated groups rarely have model companions Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-07 Özlem Beyarslan, Piotr Kowalski
We show that if G$G$ is a finitely generated group such that its profinite completion Ĝ$\widehat{G}$ is “far from being projective” (i.e., the kernel of the universal Frattini cover of Ĝ$\widehat{G}$ is not a small profinite group), then the class of existentially closed G$G$-actions on fields is not elementary. Since any infinite, finitely generated, virtually free, and not free group is “far from
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Integral Picard group of moduli of polarized K3 surfaces Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-06 Andrea Di Lorenzo, Roberto Fringuelli, Angelo Vistoli
We compute the integral Picard group of the moduli stack of polarized K3 surfaces of fixed degree whose singularities are at most rational double points, and of its coarse moduli space. We also compute the integral Picard group of the stack of quasi-polarized K3 surfaces, and of the stacky period domain.
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Quantitative Steinitz theorem: A polynomial bound Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-04 Grigory Ivanov, Márton Naszódi
The classical Steinitz theorem states that if the origin belongs to the interior of the convex hull of a set S ⊂ R d $S \subset \mathbb {R}^d$ , then there are at most 2 d $2d$ points of S $S$ whose convex hull contains the origin in the interior. Bárány, Katchalski, and Pach proved the following quantitative version of Steinitz's theorem. Let Q $Q$ be a convex polytope in R d $\mathbb {R}^d$ containing
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The divergence theorem and nonlocal counterparts Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-05 Solveig Hepp, Moritz Kassmann
We present a new proof of the classical divergence theorem in bounded domains. Our proof is based on a nonlocal analog of the divergence theorem and a rescaling argument. Main ingredients in the proof are nonlocal versions of the divergence and the normal derivative. We employ these to provide definitions of well-known nonlocal concepts such as the fractional perimeter.
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Local–global divisibility on algebraic tori Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-02 Jessica Alessandrì, Rocco Chirivì, Laura Paladino
We give a complete answer to the local–global divisibility problem for algebraic tori. In particular, we prove that given an odd prime p$p$, if T$T$ is an algebraic torus of dimension r
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Almost sure behavior of the critical points of random polynomials Bull. Lond. Math. Soc. (IF 0.9) Pub Date : 2023-12-01 Jürgen Angst, Dominique Malicet, Guillaume Poly
Let (Zk)k⩾1$(Z_k)_{k\geqslant 1}$ be a sequence of independent and identically distributed complex random variables with common distribution μ$\mu$ and let Pn(X):=∏k=1n(X−Zk)$P_n(X):=\prod _{k=1}^n (X-Z_k)$ be the associated random polynomial in C[X]$\mathbb {C}[X]$. Kabluchko established the conjecture stated by Pemantle and Rivin that the empirical measure νn$\nu _n$ associated with the critical