Inventiones mathematicae

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• Higher uniformity of arithmetic functions in short intervals II. Almost all intervals AI翻译
  作者：Matomaki, Kaisa; Radziwill, Maksym; Shao, Xuancheng; Tao, Terence; Teravainen, Joni
  作者单位：University of Turku; Northwestern University; University of Kentucky; University of California System; University of California Los Angeles; University of Cambridge
  摘要：We study higher uniformity properties of the von Mangoldt function Lambda, the M & ouml;bius function mu, and the divisor functions d(k) on short intervals(x, x+H]for almost all x is an element of[X,2X].Let Lambda(& sharp;)and d(k)(& sharp;)be suitable approximants of Lambda and d(k) ,G/ Gamma a filtered nilmanifold, and F:G/ Gamma ->& Copf;a Lipschitz function. Then our results imply for instance that when X1/3+epsilon <= H <= Xwe have, for almost all x is an element of[X,2X], sup(g is an ele...
• Symplectic L-functions and symplectic Reidemeister torsion (mod squares) AI翻译
  作者：Abdurrahman, Amina; Venkatesh, Akshay
  作者单位：Princeton University; Institute for Advanced Study - USA
  摘要：We propose (and prove under some restrictions) that the square class of the central value of the L-function of an everywhere unramified symplectic Galois representation is given by a universal cohomological formula. This phenomenon is parallel to the appearance of metaplectic groups in quantization. In the course of the proof we also establish a topological analogue of this statement, concerning Reidemeister torsion of 3-manifolds.
• The Landis conjecture on exponential decay AI翻译
  作者：Logunov, A.; Malinnikova, E.; Nadirashvili, N.; Nazarov, F.
  作者单位：Massachusetts Institute of Technology (MIT); Stanford University; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS); University System of Ohio; Kent State University; Kent State University Kent; Kent State University Salem
  摘要：Consider a solution u to Delta u + Vu = 0 on R-2, where V is real-valued, measurable and |V|<= 1. If |u(x)| <= exp (-C|x|log(1/2)|x|), |x| > 2, where C is a sufficiently large absolute constant, then u equivalent to 0.
• W*-Superrigidity for cocycle twisted group von Neumann algebras AI翻译
  作者：Donvil, Milan; Vaes, Stefaan
  作者单位：KU Leuven
  摘要：We construct countable groups G with the following new degree of W*-superrigidity: if L(G) is virtually isomorphic, in the sense of admitting a bifinite bimodule, with any other group von Neumann algebra L(Lambda), then the groups G and Lambda must be virtually isomorphic. Moreover, we allow both group von Neumann algebras to be twisted by an arbitrary 2-cocycle. We also give examples of II1 factors N that are indecomposable in every sense: they are not virtually isomorphic to any cocycle twis...
• Finite time singularities of the Kähler-Ricci flow AI翻译
  作者：Jian, Wangjian; Song, Jian; Tian, Gang
  作者单位：Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; Nanjing Institute of Geology & Paleontology, CAS; Academy of Mathematics & System Sciences, CAS; Rutgers University System; Rutgers University New Brunswick; Peking University; Peking University
  摘要：We establish the scalar curvature and distance bounds, extending Perelman's work on the Fano K & auml;hler-Ricci flow to general finite time solutions of the K & auml;hler-Ricci flow. These bounds are achieved by our Li-Yau type and Harnack estimates for weighted Ricci potential functions of the K & auml;hler-Ricci flow. We further prove that the Type I blow-ups of the finite time solution always sub-converge in Gromov-Hausdorff sense to an ancient solution on a family of analytic normal varie...
• Non-compact Riemann surfaces are equilaterally triangulable AI翻译
  作者：Bishop, Christopher J.; Rempe, Lasse
  作者单位：State University of New York (SUNY) System; Stony Brook University; University of Manchester
  摘要：We show that every open Riemann surface X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$X$\end{document} can be obtained by glueing together a countable collection of equilateral triangles, in such a way that every vertex belongs to finitely many triangles. Equivalently, X\documentclass[12pt]{minimal} \usepackage{a...
• Intermediate complex structure limit for Calabi-Yau metrics AI翻译
  作者：Li, Yang
  摘要：We study polarised degenerations of n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$n$\end{document}-dimensional Calabi-Yau hypersurfaces {F0F1 & mldr;Fm+tF=0}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} ...
• Sharp bounds on the Nusselt number in Rayleigh-Bénard convection and a bilinear estimate by Coifman-Meyer AI翻译
  作者：Chanillo, Sagun; Malchiodi, Andrea
  作者单位：Rutgers University System; Rutgers University New Brunswick; Scuola Normale Superiore di Pisa
  摘要：We prove a conjecture in fluid dynamics concerning optimal bounds for heat transportation in the infinite Prandtl number limit and for large Rayleigh number Ra\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathrm{Ra}$\end{document}, predicted in (Howard in Proceedings of the 11th International Congress of Applied ...
• The D-equivalence conjecture for hyper-Kähler varieties via hyperholomorphic bundles AI翻译
  作者：Maulik, Davesh; Shen, Junliang; Yin, Qizheng; Zhang, Ruxuan
  作者单位：Massachusetts Institute of Technology (MIT); Yale University; Peking University; Fudan University
  摘要：We show that birational hyper-K & auml;hler varieties of K3[n]-type are derived equivalent, establishing the D-equivalence conjecture in these cases. The Fourier-Mukai kernels of our derived equivalences are constructed from projectively hyperholomorphic bundles, following ideas of Markman. Our method also proves a stronger version of the D-equivalence conjecture for hyper-K & auml;hler varieties of K3[n]-type with Brauer classes.
• The sup-norm problem for newforms of large level on PGL(n) AI翻译
  作者：Toma, Radu
  作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
  摘要：Let N be a prime and phi be a Hecke-Maa ss cuspidal newform for the Hecke congruence subgroup Gamma 0(N) in SLn(R). We define a notion of the bulk Omega N of the space Gamma 0(N)\SLn(R)/SO(n) with respect to a compact set Omega subset of SLn(R). For any prime n, we prove sub-baseline bounds for the sup-norm of phi restricted to Omega N. Conditionally on GRH, we generalise this result to all n >= 2. The methods involve a new reduction theory with level structure, based on generalisations of Atk...