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New Directions in the Theory of Universal Zeta- and L-Functions
**Number Theory --- Complex Analysis --- Measure and Probability Theory**

**October 6 to October 10, 2008**

at the Department of Mathematics, Würzburg University, Germany
organized by Jörn & Rasa Steuding
**This conference is financially supported by the W.H. Ruchti-Stiftung.**This conference will be devoted to the value-distribution theory of zeta- and L-functions with an emphasis on limit theorems and universality and their applications. The phenomenon of universality is a common phenomenon in analysis whenever limit processes are involved. However, the only explicit examples of universal objects in mathematics so far are given by zeta- and L-functions: 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. In the meantime several significant extensions and generalizations of this remarkable theorem were found. Proofs of universality theorems for Dirichlet series involve methods and results from number theory, complex analysis, and often from probability theory resp. measure theory. Almost classic applications of universality theorems are functional independence (hypertranscendence) and analogues of the Riemann hypothesis (provided there are not too many zeros in the strip of universality). In the recent past interesting new classes of zeta- and L- functions were proved to be universal (e.g. L-functions to elliptic curves) and new applications to number theory were found (distribution of class numbers). Another aspect of the conference is to understand other types of universality (e.g. the classical examples of Fekete and Birkhoff) and how these match to the universality of zeta- and L-functions. The conference will be located at the Faculty of Mathematics and Computer Science at Würzburg University. Accommodation is in the nearby Schönstattzentrum Marienhöhe. Limited financial support is available! For registration or further information please contact: Jörn Steuding, Dept. Mathematics, Würzburg University, Am Hubland, D-97074 Würzburg, Germany; Tel.: +49 931 888-5008, steuding@mathematik.uni-wuerzburg.de.