The universality of Dirichlet series
by
Antanas Laurinčikas
Vilnius University, Siauliai University

The universality of given Dirichlet series means that any analytic function can be uniformly approximated on some sets by translations of that Dirichlet series. There exists the Linnik-Ibragimov conjecture that all Dirichlet series are universal. The first result in this direction was the proof by S.M.Voronin in 1975 of the universality for the Riemann zeta-function. In the report the universality of Dirichlet series of certain cusp forms, the joint universality of Lerch zeta-functions and the universality of Dirichlet series attached to finite Abelian groups will be discussed. Part of these results is joint work with Kohji Matsumoto.

Date received: April 6, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacf-21.