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One Level Density for Cubic Galois Number Fields

Part of: Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  04 January 2019

Patrick Meisner
Patrick Meisner*
Affiliation:
Tel Aviv University, 6997801 Tel Aviv, Israel Email: meisner@mail.tau.ac.il
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Abstract

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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.

Keywords

L-functionone level density

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$
Secondary: 11M26: Nonreal zeros of $zeta (s)$ and $L(s, chi)$; Riemann and other hypotheses 11M50: Relations with random matrices
Type
Article
Information
Canadian Mathematical Bulletin , Volume 62 , Issue 1 , March 2019 , pp. 149 - 167
Copyright
© Canadian Mathematical Society 2018 

Footnotes

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no. 320755.

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