Extreme values of Dirichlet polynomials with multiplicative coefficients

被引：0

作者：

Xu, Max Wenqiang ^{[1
]}

Yang, Daodao ^{[2
]}

机构：

[1] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[2] Graz Univ Technol, Inst Anal & Number Theory, Kopernikusgasse 24-2, A-8010 Graz, Austria

来源：

JOURNAL OF NUMBER THEORY | 2024年 / 258卷

基金：

奥地利科学基金会;

关键词：

Extreme value; Dirichlet polynomials; Resonance method; Multiplicative number theory; Random multiplicative function; RIEMANN ZETA-FUNCTION; SUMS;

D O I：

10.1016/j.jnt.2023.11.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study extreme values of Dirichlet polynomials with multiplicative coefficients, namely 1 � DN (t) := Df, N (t) = root N n �N f (n)nit, where f is a completely multiplicative function with |f (n)| = 1 for all n is an element of N. We use Soundararajan's resonance method to produce large values of |DN (t)| uniformly for all such f. In particular, we improve a recent result of Benatar and Nishry, where they establish weaker lower bounds and only for almost all such f. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：173 / 180

页数：8

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