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One Level Density for Cubic Galois Number Fields

  • 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 L-function, one level density
MSC Classifications: 11M06, 11M26, 11M50 show english descriptions $\zeta (s)$ and $L(s, \chi)$
Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
Relations with random matrices
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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