Value Distribution of L-Functions
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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: Riemann’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.
Author(s) :Jörn Steuding
Publish Year :2007 Publisher : Springer
You can check by ISBN10/ISBN13 : 3540265260/9783540265269
Pages :319
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