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On the One-Level Density Conjecture for Quadratic Dirichlet L-Functions

Published online by Cambridge University Press:  20 November 2018

A. E. Özlük  and
C. Snyder
A. E. Özlük
Affiliation:
Department of Mathematics and Statistics, University of Maine, Orono, Maine 04469, U.S.A. e-mail: [email protected]
C. Snyder
Affiliation:
Research Institute of Mathematics, Orono, ME 04473, U.S.A. e-mail: [email protected]
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Abstract

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In a previous article, we studied the distribution of “low–lying” zeros of the family of quadratic Dirichlet $L$–functions assuming the Generalized Riemann Hypothesis for all Dirichlet $L$–functions. Even with this very strong assumption, we were limited to using weight functions whose Fourier transforms are supported in the interval (−2, 2). However, it is widely believed that this restriction may be removed, and this leads to what has become known as the One-Level Density Conjecture for the zeros of this family of quadratic $L$-functions. In this note, we make use of Weil's explicit formula as modified by Besenfelder to prove an analogue of this conjecture.

Keywords

11M26
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 58 , Issue 4 , 01 August 2006 , pp. 843 - 858
Copyright
Copyright © Canadian Mathematical Society 2006

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