Duke Mathematical Journal

Low-lying zeros of L-functions and random matrix theory

Michael Rubinstein

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By looking at the average behavior (n-level density) of the low-lying zeros of certain families of L-functions, we find evidence, as predicted by function field analogs, in favor of a spectral interpretation of the nontrivial zeros in terms of the classical compact groups.

Article information

Duke Math. J., Volume 109, Number 1 (2001), 147-181.

First available in Project Euclid: 5 August 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M26: Nonreal zeros of $\zeta (s)$ and $L(s, \chi)$; Riemann and other hypotheses
Secondary: 11F66: Langlands $L$-functions; one variable Dirichlet series and functional equations


Rubinstein, Michael. Low-lying zeros of L -functions and random matrix theory. Duke Math. J. 109 (2001), no. 1, 147--181. doi:10.1215/S0012-7094-01-10916-2. https://projecteuclid.org/euclid.dmj/1091737225

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