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Cho, Peter J.
Lab for L-functions and arithmetic
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Dirichlet characters and low-lying zeros of L-functions

Author(s)
Cho, Peter J.Park. Jeongho
Issued Date
2020-07
DOI
10.1016/j.jnt.2019.12.001
URI
https://scholarworks.unist.ac.kr/handle/201301/31245
Fulltext
https://www.sciencedirect.com/science/article/pii/S0022314X19304019?via%3Dihub
Citation
JOURNAL OF NUMBER THEORY, v.212, pp.203 - 232
Abstract
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.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
ISSN
0022-314X
Keyword (Author)
Dirichlet characterOne-level densityn-level densityRatios conjecture
Keyword
ONE-LEVELRATIOSFAMILIESDENSITIES

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