Valuedistribution of Lfunctions Jörn Steuding

ISBN: 9783540448228

Published: January 1st 2007

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Valuedistribution of Lfunctions  by  Jörn Steuding

Valuedistribution of Lfunctions by Jörn Steuding
January 1st 2007 | ebook | PDF, EPUB, FB2, DjVu, talking book, mp3, RTF | | ISBN: 9783540448228 | 7.41 Mb

These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. In 1975, Voronin proved that any non-vanishing analytic function can be approximated uniformly by certain shifts ofMoreThese notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality.

In 1975, Voronin proved that any non-vanishing analytic function can be approximated uniformly by certain shifts of the Riemann zeta-function in the critical strip. This spectacular universality property has a strong impact on the zero-distribution: Riemannbs hypothesis is true if and only if the Riemann zeta-function can approximate itself uniformly (in the sense of Voronin).Meanwhile universality is proved for a large zoo of Dirichlet series, and it is conjectured that all reasonable L-functions are universal.

In these notes we prove universality for polynomial Euler products. Our approach follows mainly Bagchis probabilistic method. We further discuss related topics as, e.g., almost periodicity, density estimates, Nevanlinna theory, and functional independence.



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