Random matrix theory and discrete moments of the Riemann zeta function

Author: Hughes C.P.¹

Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 2907-2917(11)

Publisher: Institute of Physics Publishing

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Abstract:

We calculate the discrete moments of the characteristic polynomial of a random unitary matrix, evaluated a small distance away from an eigenangle. Such results allow us to make conjectures about similar moments for the Riemann zeta function, and provide a uniform approach to understanding moments of the zeta function and its derivative.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Current address: American Institute of Mathematics, 360 Portage Ave, Palo Alto, CA 94306, USA.

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