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

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

2009-10-27

arxiv.org/abs/0910.5063v3

Compos. Math., Vol. 147, 2011, No. 1, pp. 1-18

Mathematics

Number Theory

15 pages. Revisions have been made with accordance to the referee's report and it is to appear in Compos. Math

Scientific paper

In this paper, we prove some one level density results for 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.

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