2020

最新文章

• Fourier uniformity of bounded multiplicative functions in short intervals on average AI翻译
  作者：Matomaki, Kaisa; Radziwill, Maksym; Tao, Terence
  作者单位：University of Turku; California Institute of Technology; University of California System; University of California Los Angeles
  摘要：Let lambda\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda $$\end{document}, integral X2Xsup alpha n-ary sumation x<= x+H lambda(n)e(-alpha n)dx=o(XH)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \u...
• On the Lebesgue measure of the Feigenbaum Julia set AI翻译
  作者：Dudko, Artem; Sutherland, Scott
  作者单位：Polish Academy of Sciences; Institute of Mathematics of the Polish Academy of Sciences; State University of New York (SUNY) System; Stony Brook University
  摘要：We show that the Julia set of the Feigenbaum polynomial has Hausdorff dimension less than 2 (and consequently it has zero Lebesgue measure). This solves a long-standing open question.
• Multiple zeta values in deformation quantization AI翻译
  作者：Banks, Peter; Panzer, Erik; Pym, Brent
  作者单位：University of Oxford; University of Edinburgh; McGill University
  摘要：Kontsevich's 1997 formula for the deformation quantization of Poisson brackets is a Feynman expansion involving volume integrals over moduli spaces of marked disks. We develop a systematic theory of integration on these moduli spaces via suitable algebras of polylogarithms, and use it to prove that Kontsevich's integrals can be expressed as integer-linear combinations of multiple zeta values. Our proof gives a concrete algorithm for calculating the integrals, which we have used to produce the ...
• Full factors, bicentralizer flow and approximately inner automorphisms AI翻译
  作者：Marrakchi, Amine
  作者单位：Ecole Normale Superieure de Lyon (ENS de LYON)
  摘要：We show that a factor M is full if and only if the C*-algebra generated by its left and right regular representations contains the compact operators. We prove that the bicentralizer flow of a type III1 factor is always ergodic. As a consequence, for any type III1 factor M and any lambda is an element of]0, 1], there exists an irreducible AFD type III lambda subfactor with expectation in M. Moreover, any type III1 factor M which satisfies M congruent to M (circle times) over bar R-lambda for so...
• When Kloosterman sums meet Hecke eigenvalues AI翻译
  作者：Xi, Ping
  作者单位：Xi'an Jiaotong University
  摘要：By elaborating a two-dimensional Selberg sieve with asymptotics and equidistributions of Kloosterman sums from l\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell $$\end{document}-adic cohomology, as well as a Bombieri-Vinogradov type mean value theorem for Kloosterman sums in arithmetic progressions, it is prove...
• An effective Chebotarev density theorem for families of number fields, with an application to l-torsion in class groups AI翻译
  作者：Pierce, Lillian B.; Turnage-Butterbaugh, Caroline L.; Wood, Melanie Matchett
  作者单位：Duke University; Institute for Advanced Study - USA; Carleton College; University of California System; University of California Berkeley
  摘要：We prove a new effective Chebotarev density theorem for Galois extensions L/Q that allows one to count small primes (even as small as an arbitrarily small power of the discriminant of L); this theorem holds for the Galois closures of almost all number fields that lie in an appropriate family of field extensions. Previously, applying Chebotarev in such small ranges required assuming the Generalized Riemann Hypothesis. The error term in this new Chebotarev density theorem also avoids the effect ...