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# One Level Density for Cubic Galois Number Fields

Published:2018-06-07

• Patrick Meisner,
Tel Aviv University, 6997801 Tel Aviv, Israel
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## Abstract

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.
 Keywords: L-function, one level density
 MSC Classifications: 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

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