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

Published:2006-08-01
Printed: Aug 2006
• A. E. Õzlük
• C. Snyder
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## Abstract

In a previous article, we studied the distribution of low-lying" zeros of the family of quad\-ratic 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.
 MSC Classifications: 11M26 - Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses

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