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3 results

One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$-functions
Part of
Peng Gao, Liangyi Zhao
Journal:

Canadian Journal of Mathematics / Volume 72 / Issue 2 / April 2020

Published online by Cambridge University Press:

30 August 2019, pp. 427-454

Print publication:

April 2020
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In this paper we prove some one-level density results for the low-lying zeros of families of quadratic and quartic Hecke $L$-functions of the Gaussian field. As corollaries, we deduce that at least 94.27% and 5%, respectively, of the members of the quadratic family and the quartic family do not vanish at the central point.

One Level Density for Cubic Galois Number Fields
Part of
- Zeta and $L$-functions: analytic theory
Patrick Meisner
Journal:

Canadian Mathematical Bulletin / Volume 62 / Issue 1 / March 2019

Published online by Cambridge University Press:

04 January 2019, pp. 149-167

Print publication:

March 2019
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Katz and Sarnak predicted that the one level density of the zeros of a family of L-functions would fall into one of five categories. In this paper, we show that the one level density for L-functions attached to cubic Galois number fields falls into the category associated with unitary matrices.

One level density of low-lying zeros of families of L-functions
Part of
Peng Gao, Liangyi Zhao
Journal:

Compositio Mathematica / Volume 147 / Issue 1 / January 2011

Published online by Cambridge University Press:

07 September 2010, pp. 1-18

Print publication:

January 2011
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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.

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3 results

One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$-functions

One Level Density for Cubic Galois Number Fields

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