Value-Distribution of L-Functions 2024 pdf epub mobi 电子书

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发表于2024-07-07

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出版者:Springer Verlag

作者:Steuding, Jrn

出品人:

页数:336

译者:

出版时间:

价格:$ 90.34

装帧:Pap

isbn号码:9783540265269

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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 of the Riemann zeta-function in the critical strip. This spectacular universality property has a strong impact on the zero-distribution: Riemanna (TM)s 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 Bagchi's probabilistic method. We further discuss related topics as, e.g., almost periodicity, density estimates, Nevanlinna theory, and functional independence.

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