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One level density of low-lying zeros of families of L-functions

Part of: Algebraic number theory: global fields Zeta and $L$-functions: analytic theory Discontinuous groups and automorphic forms Exponential sums and character sums

Published online by Cambridge University Press:  07 September 2010

Peng Gao  and
Liangyi Zhao
Peng Gao
Affiliation:
Division of Mathematical Science, School of Physics & Mathematical Science, Nanyang Technological University, Singapore 637371 (email: [email protected])
Liangyi Zhao
Affiliation:
Division of Mathematical Science, School of Physics & Mathematical Science, Nanyang Technological University, Singapore 637371 (email: [email protected])
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Abstract

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In this paper, we prove some one level density results for the low-lying zeros of families of L-functions. More specifically, the families under consideration are that of L-functions of holomorphic Hecke eigenforms of level 1 and weight k twisted with quadratic Dirichlet characters and that of cubic and quartic Dirichlet L-functions.

Keywords

one level densitylow-lying zerosHecke eigenformsquadratic Dirichlet characterscubic Dirichlet charactersquartic Dirichlet characters

MSC classification

Secondary: 11F11: Holomorphic modular forms of integral weight 11L40: Estimates on character sums 11M06: $zeta (s)$ and $L(s, chi)$ 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses 11M50: Relations with random matrices 11R16: Cubic and quartic extensions
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 1 , January 2011 , pp. 1 - 18
Copyright
Copyright © Foundation Compositio Mathematica 2010

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