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.

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)

Dirichlet Series and Polynomial Euler Products.- Interlude: Results from Probability Theory.- Limit Theorems.- Universality.- The Selberg Class.- Value-Distribution in the Complex Plane.- The Riemann Hypothesis.- Effective Results.- Consequences of Universality.- Dirichlet Series with Periodic Coefficients.- Joint Universality.- L-Functions of Number Fields.