Nonvanishing of Dirichlet L-functions, II

被引：0

作者：

Rizwanur Khan

Djordje Milićević

Hieu T. Ngo

机构：

[1] University of Mississippi,Mathematics Department

[2] Bryn Mawr College,Department of Mathematics

[3] Max-Planck-Institut für Mathematik,undefined

[4] Vietnam Institute for Advanced Study in Mathematics,undefined

来源：

Mathematische Zeitschrift | 2022年 / 300卷

关键词：

-Functions; Dirichlet characters; Nonvanishing; Mollifier; Kloosterman sums; 11M20;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We show that for at least 513\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{5}{13}$$\end{document} of the primitive Dirichlet characters χ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\chi $$\end{document} of large prime modulus, the central value L(12,χ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L(\frac{1}{2},\chi )$$\end{document} does not vanish, improving on the previous best known result of 38\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{3}{8}$$\end{document}.

引用

页码：1603 / 1613

页数：10