Mean values of L-functions and symmetry

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Recently Katz and Sarnak introduced the idea of a symmetry group attached to a family of L-functions, and they gave strong evidence that the symmetry group governs many properties of the distribution of zeros of the L-functions. We consider the mean-values of the L-functions and the mollified mean-square of the L-functions and find evidence that these are also governed by the symmetry group. We use recent work of Keating and Snaith to give a complete description of these mean values. We find a connection to the Barnes-Vignéras $Γ_2$-function and to a family of self-similar functions.
23 pages, 6 figures

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Number Theory, Mathematical Physics, 11M06; 11F66; 81Q50

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http://salesiana.dossiersoluciones.com/handle/123456789/79601

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9912107
 http://arxiv.org/abs/math/9912107

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arXiv