Ebook: Value-Distribution of L-Functions

Career details of the author:

1996-1999: assistant of Prof. G.J. Rieger at Hanover University

1999: PhD at Hanover University under supervision of Prof. Dr. G.J. Rieger

1999-2004: assistant of Prof. Dr. W. Schwarz and Prof. Dr. J. Wolfart at Frankfurt University

2004: Habilitation at Frankfurt University (venia legendi)

2004-today: ‘Ramon y Cajal’-investigador at Universidad Autonoma de Madrid (research fellow)

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These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.