Dirichlet characters and low-lying zeros of L-functions

JOURNAL OF NUMBER THEORY

卷:212

Article

Cho, Peter J.¹  Park, Jeongho² 

[1] Ulsan Natl Inst Sci & Technol, Dept Math Sci, Ulsan, South Korea

[2] Pohang Univ Sci & Technol, Dept Math, Pohang, South Korea

关键词: Dirichlet character;    One-level density;    n-level density;    Ratios conjecture;   

DOI  :  10.1016/j.jnt.2019.12.001

来源: Elsevier

【 摘 要 】

Let r be a positive integer >= 2. We consider a family of primitive Dirichlet characters of order r with conductor co-prime to r. For this family, we compute the one-level density with explicit lower order terms in two ways, using Weil's explicit formula and the Ratios conjecture. Also, the n. level density for the family twisted by a fixed cuspidal automorphic representation pi of GL(M) (A(Q)) is obtained. It turns out that, when r >= 3, the symmetry type for our family is always unitary. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free