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Value-Distribution of L-Functions (Paperback)

Author: Steuding, Jorn

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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.


Publisher Springer Verlag
Mfg Part# 9783540265269
SKU 202846678
Format Paperback
ISBN10 3540265260
Release Date 11/19/2007
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