• Q. J. Math. (IF 0.704) Pub Date : 2020-06-30
Brendan Owens

We exhibit an infinite family of rational homology balls, which embed smoothly but not symplectically in the complex projective plane. We also obtain a new lattice embedding obstruction from Donaldson’s diagonalization theorem and use this to show that no two of our examples may be embedded disjointly.

更新日期：2020-06-30
• Q. J. Math. (IF 0.704) Pub Date : 2020-06-29
Javier Pliego

We show that almost every positive integer can be expressed as a sum of four squares of integers represented as the sums of three positive cubes.

更新日期：2020-06-29
• Q. J. Math. (IF 0.704) Pub Date : 2020-06-27
Manuel Krannich

By work of Berglund and Madsen, the rings of rational characteristic classes of fibrations and smooth block bundles with fibre |$D^{2n}\sharp (S^n\times S^n)^{\sharp g}$|⁠, relative to the boundary, are for |$2n\ge 6$| independent of |$g$| in degrees |$*\le (g-6)/2$|⁠. In this note, we explain how this range can be improved to |$*\le g-2$| using cohomological vanishing results due to Borel and the

更新日期：2020-06-27
• Q. J. Math. (IF 0.704) Pub Date : 2020-06-25
Mounir Hajli

In this paper, we study a large class of zeta functions. We evaluate explicitly the special values of these zeta functions and the associated derivatives at |$0$|⁠. As an application, we recover several results on the zeta functions defined by two polynomials already obtained in the literature.

更新日期：2020-06-25
• Q. J. Math. (IF 0.704) Pub Date : 2020-06-22
Peter Newstead; Montserrat Teixidor i Bigas

It is well known that there are no stable bundles of rank greater than 1 on the projective line. In this paper, our main purpose is to study the existence problem for stable coherent systems on the projective line when the number of sections is larger than the rank. We include a review of known results, mostly for a small number of sections.

更新日期：2020-06-25
• Q. J. Math. (IF 0.704) Pub Date : 2020-06-22
G Lusztig

Let u be a unipotent element in the totally positive part of a complex reductive group. We consider the intersection of the Springer fibre at u with the totally positive part of the flag manifold. We show that this intersection has a natural cell decomposition which is part of the cell decomposition (Rietsch) of the totally positive flag manifold.

更新日期：2020-06-23
• Q. J. Math. (IF 0.704) Pub Date : 2020-06-17
Christopher Voll

We produce explicit formulae for various ideal zeta functions associated to the members of an infinite family of class-|$2$|-nilpotent Lie rings, introduced in M. N. Berman, B. Klopsch and U. Onn (A family of class-2 nilpotent groups, their automorphisms and pro-isomorphic zeta functions, Math. Z. 290 (2018), 909935), in terms of Igusa functions. As corollaries we obtain information about analytic

更新日期：2020-06-23
• Q. J. Math. (IF 0.704) Pub Date : 2020-06-17
Gareth Boxall

We obtain a non-trivial special case of Zilber’s quasiminimality conjecture for the complex exponential field. Specifically, we deal with those subsets of |$\mathbb{C}$| defined by formulas of the form |$\exists \bar{y}(P(x,\bar{y})=0)$|⁠, where |$P$| is a term formed from the language |$\{+,\times ,\exp \}$| together with parameters from |$\mathbb{C}$|⁠.

更新日期：2020-06-23
• Q. J. Math. (IF 0.704) Pub Date : 2020-06-17
Kevin Beanland; Ryan M Causey

A bounded linear operator |$U$| between Banach spaces is universal for the complement of some operator ideal |$\mathfrak{J}$| if it is a member of the complement and it factors through every element of the complement of |$\mathfrak{J}$|⁠. In the first part of this paper, we produce new universal operators for the complements of several ideals, and give examples of ideals whose complements do not admit

更新日期：2020-06-23
• Q. J. Math. (IF 0.704) Pub Date : 2020-06-17
Hao Chang

Let |$\mathscr{B}_0({\mathcal{G}})\subseteq k\,{\mathcal{G}}$| be the principal block algebra of the group algebra |$k\,{\mathcal{G}}$| of an infinitesimal group scheme |${\mathcal{G}}$| over an algebraically closed field |$k$| of characteristic |${\operatorname{char}}(k)=:p\geq 3$|⁠. We calculate the restricted Lie algebra structure of the first Hochschild cohomology |${\mathcal{L}}:={\operatorna 更新日期：2020-06-17 • Q. J. Math. (IF 0.704) Pub Date : 2020-06-15 Sebastian Baader; Luca Studer; Roger Züst It is known that the surface of a cone over the unit disc with large height has smaller distortion than the standard embedding of the 2-sphere in |$\mathbb{R}^3$|⁠. In this note we show that distortion minimizers exist among convex embedded 2-spheres and have uniformly bounded eccentricity. Moreover, we prove that |$\pi /2$| is a sharp lower bound on the distortion of embedded closed surfaces of positive 更新日期：2020-06-15 • Q. J. Math. (IF 0.704) Pub Date : 2020-06-08 Oliver Leigh We further the study of the Donaldson–Thomas theory of the banana 3-folds which were recently discovered and studied by Bryan [3]. These are smooth proper Calabi–Yau 3-folds which are fibred by Abelian surfaces such that the singular locus of a singular fibre is a non-normal toric curve known as a ‘banana configuration’. In [3], the Donaldson–Thomas partition function for the rank 3 sub-lattice generated 更新日期：2020-06-08 • Q. J. Math. (IF 0.704) Pub Date : 2020-06-04 L D Klausner; T Weinert We analyse partitions of products with two ordered factors in two classes where both factors are countable or well-ordered and at least one of them is countable. This relates the partition properties of these products to cardinal characteristics of the continuum. We build on work by Erd̋s, Garti, Jones, Orr, Rado, Shelah and Szemerédi. In particular, we show that a theorem of Jones extends from the 更新日期：2020-06-04 • Q. J. Math. (IF 0.704) Pub Date : 2020-05-08 Rafal Komendarczyk; Robin Koytcheff; Ismar Volić We use rational formality of configuration spaces and the bar construction to study the cohomology of the space of braids in dimension four or greater. We provide a diagram complex for braids and a quasi-isomorphism to the de Rham cochains on the space of braids. The quasi-isomorphism is given by a configuration space integral followed by Chen’s iterated integrals. This extends results of Kohno and 更新日期：2020-05-08 • Q. J. Math. (IF 0.704) Pub Date : 2020-04-28 Tiberiu Coconeţ; Andrei Marcus; Constantin-Cosmin Todea Let |$(\mathcal{K},\mathcal{O},k)$| be a |$p$|-modular system where |$p$| is a prime and |$k$| algebraically closed, let |$b$| be a |$G$|-invariant block of the normal subgroup |$H$| of a finite group |$G$|⁠, having defect pointed group |$Q_\delta$| in |$H$| and |$P_\gamma$| in |$G$| and consider the block extension |$b\mathcal{O}G$|⁠. One may attach to |$b$| an extended local category |$\mathcal{E}_{(b

更新日期：2020-04-28
• Q. J. Math. (IF 0.704) Pub Date : 2020-02-10
Wang F.

AbstractWe establish integral formulas and sharp two-sided bounds for the Ricci curvature, mean curvature and second fundamental form on a Riemannian manifold with boundary. As applications, sharp gradient and Hessian estimates are derived for the Dirichlet and Neumann eigenfunctions.

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2020-02-06
M Cafferata; A Perelli; A Zaccagnini

We first prove an extension of the Bourgain–Sarnak–Ziegler theorem, relaxing some conditions and giving quantitative estimates. Then we apply our extension to bound certain exponential sums, where the coefficients come from modular forms and the exponential involves polynomial sequences of any degree.

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2020-02-05
Alexander Kupers

We prove a homological stability theorem for unlinked circles in |$3$|-manifolds and give an application to certain groups of diffeomorphisms of 3-manifolds.

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2020-02-05
Christopher Attenborough; Michael Bate; Maike Gruchot; Alastair Litterick; Gerhard Röhrle

Let |$K$| be a reductive subgroup of a reductive group |$G$| over an algebraically closed field |$k$|⁠. The notion of relative complete reducibility, introduced in [M. Bate, B. Martin, G. Röhrle, R. Tange, Complete reducibility and conjugacy classes of tuples in algebraic groups and Lie algebras, Math. Z.269 (2011), no. 1, 809–832], gives a purely algebraic description of the closed |$K$|-orbits in

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2020-01-25
Shuichi Sato

We establish a characterization of the Hardy spaces on the homogeneous groups in terms of the Littlewood–Paley functions. The proof is based on vector-valued inequalities shown by applying the Peetre maximal function.

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2020-01-25
Laustsen N, Troitsky V.

AbstractWe characterize the Archimedean vector lattices that admit a positively homogeneous continuous function calculus by showing that the following two conditions are equivalent for each $n$-tuple $\boldsymbol{x} = (x_1,\ldots ,x_n)\in X^n$, where $X$ is an Archimedean vector lattice and $n\in{\mathbb{N}}$: • there is a vector lattice homomorphism $\Phi _{\boldsymbol{x}}\colon H_n\to X$ such that

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2020-01-23

The Alternative Hypothesis (AH) concerns a hypothetical and unlikely picture of how zeros of the Riemann zeta function are spaced, which one would like to rule out. In the Alternative Hypothesis, the renormalized distance between non-trivial zeros is supposed to always lie at a half integer. It is known that the Alternative Hypothesis is compatible with what is known about the pair correlation function

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2020-01-20
Dawei Chen

Three decades ago Cornalba and Harris proved a fundamental positivity result for divisor classes associated to families of stable curves. In this paper we establish an analogous positivity result for divisor classes associated to families of stable differentials.

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2019-12-27
Bertrand J Guillou; J Peter May; Mona Merling; Angélica M Osorno

We give an operadic definition of a genuine symmetric monoidal |$G$|-category, and we prove that its classifying space is a genuine |$E_\infty$||$G$|-space. We do this by developing some very general categorical coherence theory. We combine results of Corner and Gurski, Power and Lack to develop a strictification theory for pseudoalgebras over operads and monads. It specializes to strictify genuine

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2019-12-20
Michel Gros; Kaneda Masaharu

Pour un groupe algébrique semi-simple simplement connexe sur un corps algébriquement clos de caractéristique positive, nous avons précédemment construit un scindage de l’endomorphisme de Frobenius sur son algèbre des distributions. Nous généralisons la construction au cas de des groupes réductifs connexes et en dégageons les corollaires correspondants.

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2019-12-18
Funayoshi K, Koda Y.

AbstractAn automorphism $f$ of a closed orientable surface $\Sigma$ is said to be extendable over the 3-sphere $S^3$ if $f$ extends to an automorphism of the pair $(S^3, \Sigma )$ with respect to some embedding $\Sigma \hookrightarrow S^3$. We prove that if an automorphism of a genus-2 surface $\Sigma$ is extendable over $S^3$, then $f$ extends to an automorphism of the pair $(S^3, \Sigma )$ with

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2019-12-10
Castillo J, Moreno Y.

AbstractWe introduce and study the notion of space of almost universal complemented disposition (a.u.c.d.) as a generalization of Kadec space. We show that every Banach space with separable dual is isometrically contained as a $1$-complemented subspace of a separable a.u.c.d. space and that all a.u.c.d. spaces with $1$-finite dimensional decomposition (FDD) are isometric and contain isometric $1$-complemented

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2019-12-06
FernÁndez-Alcober G, Jezernik U.

AbstractLet $G$ be a $p$-group of maximal class and order $p^n$. We determine whether or not the Bogomolov multiplier ${\operatorname{B}}_0(G)$ is trivial in terms of the lower central series of $G$ and $P_1 = C_G(\gamma _2(G) / \gamma _4(G))$. If in addition $G$ has positive degree of commutativity and $P_1$ is metabelian, we show how understanding ${\operatorname{B}}_0(G)$ reduces to the simpler

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2019-12-05
Meng X.

AbstractNumerical experiments suggest that there are more prime factors in certain arithmetic progressions than others. Greg Martin conjectured that the function $\sum _{n\leq x, n\equiv 1 \bmod 4} \omega (n)-\sum _{n\leq x, n\equiv 3 \bmod 4} \omega (n)$ will attain a constant sign as $x\rightarrow \infty$, where $\omega (n)$ is the number of distinct prime factors of $n$. In this paper, we prove

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2019-12-02
Blanca F Besoy; Fernando Cobos

We derive interpolation formulae for the measure of non-compactness of operators interpolated by logarithmic methods with |$\theta = 0,1$| between quasi-Banach spaces. Applications are given to operators between Lorentz–Zygmund spaces.

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2019-11-29
Peter Mayr; Nik Ruškuc

Let |$K$| be a commutative Noetherian ring with identity, let |$A$| be a |$K$|-algebra and let |$B$| be a subalgebra of |$A$| such that |$A/B$| is finitely generated as a |$K$|-module. The main result of the paper is that |$A$| is finitely presented (resp. finitely generated) if and only if |$B$| is finitely presented (resp. finitely generated). As corollaries, we obtain: a subring of finite index

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2019-11-20
Marco Freibert; Lothar Schiemanowski; Hartmut Weiss

We study the spinor flow on homogeneous spin manifolds. After providing the general setup we discuss the homogeneous spinor flow in dimension three and on almost abelian Lie groups in detail. As a further example, the flag manifold in dimension six is treated.

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2019-11-20
Sartori A.

AbstractWe study the mass distribution of Laplacian eigenfunctions at Planck scale for the standard flat torus $\mathbb{T}^2=\mathbb{R}^2/\mathbb{Z}^2$. By averaging over the ball centre, we use Bourgain’s de-randomization to compare the mass distribution of toral eigenfunctions to the mass distribution of random waves in growing balls around the origin. We then classify all possible limiting distributions

更新日期：2020-04-17
• Q. J. Math. (IF 0.704) Pub Date : 2020-04-13
Morten Lüders

We study the deformations of the Chow group of zerocycles of the special fibre of a smooth scheme over a Henselian discrete valuation ring. Our main tools are Bloch’s formula and differential forms. As a corollary we get an algebraization theorem for thickened zero cycles previously obtained using idelic techniques. In the course of the proof we develop moving lemmata and Lefschetz theorems for cohomology

更新日期：2020-04-13
• Q. J. Math. (IF 0.704) Pub Date : 2020-04-03
Titus Hilberdink

In this paper, we study entire functions whose maximum on a disc of radius |$r$| grows like |$e^{h(\log r)}$| for some function |$h(\cdot )$|⁠. We show that this is impossible if |$h^{\prime \prime }(r)$| tends to a limit as |$r\to \infty$|⁠, thereby solving a problem of Hayman from 1966. On the other hand, we show that entire functions can, under some mild smoothness conditions, grow like |$\textrm{e}^{h(\log 更新日期：2020-04-03 • Q. J. Math. (IF 0.704) Pub Date : 2020-04-02 Matej Brešar Three problems connecting functional identities to the recently introduced notion of a zero Lie product determined Banach algebra are discussed. The first one concerns commuting linear maps, the second one concerns derivations that preserve commutativity and the third one concerns bijective commutativity preserving linear maps. 更新日期：2020-04-02 • Q. J. Math. (IF 0.704) Pub Date : 2020-04-01 Sergei V Konyagin; Sergey V Makarychev; Igor E Shparlinski; Ilya V Vyugin We sharpen the bounds of J. Bourgain, A. Gamburd and P. Sarnak (2016) on the possible number of nodes outside the ‘giant component’ and on the size of individual connected components in the suitably defined functional graph of Markoff triples modulo |$p$|⁠. This is a step towards the conjecture that there are no such nodes at all. 更新日期：2020-04-01 • Q. J. Math. (IF 0.704) Pub Date : 2020-03-17 Jason Bell; Daryl Funk; Byoung Du Kim; Dillon Mayhew Let |$M$| be a representable matroid on |$n$| elements. We give bounds, in terms of |$n$|⁠, on the least positive characteristic and smallest field over which |$M$| is representable. 更新日期：2020-03-17 • Q. J. Math. (IF 0.704) Pub Date : 2020-03-17 Teresa Conde The Gabriel–Roiter measure is used to give an alternative proof of the finiteness of the representation dimension for Artin algebras, a result established by Iyama in 2002. The concept of Gabriel–Roiter measure can be extended to abelian length categories and every such category has multiple Gabriel–Roiter measures. Using this notion, we prove the following broader statement: given any object |$X$| 更新日期：2020-03-17 • Q. J. Math. (IF 0.704) Pub Date : 2020-03-12 Niclas Technau; Agamemnon Zafeiropoulos AbstractLet$(n_k)_{k=1}^{\infty }$be a lacunary sequence of integers. We show that if$\mu$is a probability measure on$[0,1)$such that$|\widehat{\mu }(t)|\leq c|t|^{-\eta }$, then for$\mu$-almost all$x$, the discrepancy$D_N(n_kx)$satisfies $$\begin{equation*}\frac{1}{4} \leq \limsup_{N\to\infty}\frac{N D_N(n_kx)}{\sqrt{N\log\log N}} \leq C\end{equation*}$$for some constant$C>0$. This proves 更新日期：2020-03-12 • Q. J. Math. (IF 0.704) Pub Date : 2020-02-25 María D Acosta; Pablo Galindo; Luiza A Moraes We discuss the continuity of the composition on several spaces of holomorphic mappings on open subsets of a complex Banach space. On the Fréchet space of entire mappings that are bounded on bounded sets, the composition turns out to be even holomorphic. In such a space, we consider linear subspaces closed under left and right composition. We discuss the relationship of such subspaces with ideals of 更新日期：2020-02-25 • Q. J. Math. (IF 0.704) Pub Date : 2020-02-24 Miguel A Maldonado; Miguel A Xicoténcatl The mapping class group |$\Gamma ^k(N_g)$| of a non-orientable surface with punctures is studied via classical homotopy theory of configuration spaces. In particular, we obtain a non-orientable version of the Birman exact sequence. In the case of |${\mathbb{R}} \textrm{P}^2$|⁠, we analyze the Serre spectral sequence of a fiber bundle |$F_k({\mathbb{R}}{\textrm{P}}^{2}) / \Sigma _k \to X_k \to BSO(3)$| 更新日期：2020-02-24 • Q. J. Math. (IF 0.704) Pub Date : 2020-02-07 João Marcos do Ó; Abiel Costa Macedo; José Francisco de Oliveira In a classical work (Ann. Math.128, (1988) 385–398), D. R. Adams proved a sharp Trudinger–Moser inequality for higher-order derivatives. We derive a sharp Adams-type inequality and Sobolev-type inequalities associated with a class of weighted Sobolev spaces that is related to a Hardy-type inequality. 更新日期：2020-02-07 • Q. J. Math. (IF 0.704) Pub Date : 2020-02-05 J D Maitland Wright; Kazuyuki Saitô We exhibit a wild monotone complete C*-algebra which is a hyperfinite factor but is not an injective C*-algebra. 更新日期：2020-02-05 • Q. J. Math. (IF 0.704) Pub Date : 2020-02-03 Giuseppe Negro We provide an asymptotic formula for the maximal Strichartz norm of small solutions to the cubic wave equation in Minkowski space. The leading coefficient is given by Foschi’s sharp constant for the linear Strichartz estimate. We calculate the constant in the second term, which differs depending on whether the equation is focussing or defocussing. The sign of this coefficient also changes accordingly 更新日期：2020-02-03 • Q. J. Math. (IF 0.704) Pub Date : 2020-02-03 Arturo Giles Flores; O N Silva; J Snoussi We study the behavior of limits of tangents in topologically equivalent spaces. In the context of families of generically reduced curves, we introduce the |$s$|-invariant of a curve and we show that in a Whitney equisingular family with the property that the |$s$|-invariant is constant along the parameter space, the number of tangents of each curve of the family is constant. In the context of families 更新日期：2020-02-03 • Q. J. Math. (IF 0.704) Pub Date : 2020-02-03 Bo-Hae Im; Michael Larsen Let |$f\in{\mathbb{Q}}(x)$| be a non-constant rational function. We consider ‘Waring’s problem for |$f(x)$|⁠,’ i.e., whether every element of |${\mathbb{Q}}$| can be written as a bounded sum of elements of |$\{f(a)\mid a\in{\mathbb{Q}}\}$|⁠. For rational functions of degree |$2$|⁠, we give necessary and sufficient conditions. For higher degrees, we prove that every polynomial of odd degree and every 更新日期：2020-02-03 • Q. J. Math. (IF 0.704) Pub Date : 2020-01-11 Jack Smith We give a short new computation of the quantum cohomology of an arbitrary smooth (semiprojective) toric variety |$X$|⁠, by showing directly that the Kodaira–Spencer map of Fukaya–Oh–Ohta–Ono defines an isomorphism onto a suitable Jacobian ring. In contrast to previous results of this kind, |$X$| need not be compact. The proof is based on the purely algebraic fact that a class of generalized Jacobian 更新日期：2020-01-11 • Q. J. Math. (IF 0.704) Pub Date : 2019-06-22 Lee E. A variety that contains continuum many subvarieties is said to be huge. A sufficient condition is established under which an involution monoid generates a variety that is huge by virtue of its lattice of subvarieties order-embedding the power set lattice of the positive integers. Based on this result, several examples of finite involution monoids with extreme varietal properties are exhibited. These 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-07-03 Bringmann K, Jenkins P, Kane B. In this paper, we study polar harmonic Maass forms of negative integral weight. Using work of Fay, we construct Poincaré series which span the space of such forms and show that their elliptic coefficients exhibit duality properties which are similar to the properties known for Fourier coefficients of harmonic Maass forms and weakly holomorphic modular forms. 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-07-15 Lauret J, Will C. We study the natural functional$F=\frac {\operatorname {scal}^2}{|\operatorname {Ric}|^2}$on the space of all non-flat left-invariant metrics on all solvable Lie groups of a given dimension$n$. As an application of properties of the beta operator, we obtain that solvsolitons are the only global maxima of$F$restricted to the set of all left-invariant metrics on a given unimodular solvable Lie group 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-07-15 Fino A, Rollenske S, Ruppenthal J. It is conjectured that the Dolbeault cohomology of a complex nilmanifold$X$is computed by left-invariant forms. We prove this under the assumption that$X$is suitably foliated in toroidal groups and deduce that the conjecture holds in real dimension up to six. Our approach generalizes previous methods, where the existence of a holomorphic fibration was a crucial ingredient. 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-07-15 Kwon M, Zehmisch K. We introduce the concept of fittings to symplectic fillings of the unit cotangent bundle of odd-dimensional spheres. Assuming symplectic asphericity we show that all fittings are diffeomorphic to the respective unit co-disc bundle. 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-07-15 González J, Grant M, Vandembroucq L. We develop a theory of generalized Hopf invariants in the setting of sectional category. In particular, we show how Hopf invariants for a product of fibrations can be identified as shuffle joins of Hopf invariants for the factors. Our results are applied to the study of Farber’s topological complexity for two-cell complexes, as well as to the construction of a counterexample to the analogue for topological 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-07-16 Jones G, Kirby J, Le Gal O, et al. Given a collection$\mathcal {A}$of holomorphic functions, we consider how to describe all the holomorphic functions locally definable from$\mathcal {A}$. The notion of local definability of holomorphic functions was introduced by Wilkie, who gave a complete description of all functions locally definable from$\mathcal {A}$in the neighbourhood of a generic point. We prove that this description is 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-07-24 Achar P, Hardesty W. In this paper, we carry out several computations involving graded (or${{\mathbb {G}}_{\textrm {m}}}$-equivariant) perverse-coherent sheaves on the nilpotent cone of a reductive group in good characteristic. In the first part of the paper, we compute the weight of the${{\mathbb {G}}_{\textrm {m}}}$-action on certain normalized (or ‘canonical’) simple objects, confirming an old prediction of Ostrik 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-08-27 Beirne P. In this paper, we prove a formula for the 2-head of the colored Jones polynomial for an infinite family of pretzel knots. Following Hall, the proof utilizes skein-theoretic techniques and a careful examination of higher order stability properties for coefficients of the colored Jones polynomial. 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-09-10 Banks W, Friedlander J, Pomerance C, et al. In an earlier paper we considered the distribution of integers$n$for which Euler’s totient function at$n$has all small prime factors. Here we obtain an improvement that is likely to be best possible. 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-10-04 Basu S, Lerario A, Natarajan A. Given a sequence$\{Z_d\}_{d\in \mathbb{N}}$of smooth and compact hypersurfaces in${\mathbb{R}}^{n-1}$, we prove that (up to extracting subsequences) there exists a regular definable hypersurface$\Gamma \subset {\mathbb{R}}\textrm{P}^n$such that each manifold$Z_d$is diffeomorphic to a component of the zero set on$\Gamma$of some polynomial of degree$d$. (This is in sharp contrast with the case 更新日期：2020-01-04 • Q. J. Math. (IF 0.704) Pub Date : 2019-09-26 Heap W, Radziwiłł M, Soundararajan K. We establish sharp upper bounds for the$2k$th moment of the Riemann zeta function on the critical line, for all real$0 \leqslant k \leqslant 2\$. This improves on earlier work of Ramachandra, Heath-Brown and Bettin–Chandee–Radziwiłł.

更新日期：2020-01-04
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