Petersburg Department of Steklov Institute of Mathematics

PREPRINT 15(II)/1999

THE RANKIN CONVOLUTIONS AND DIRICHLET SERIES. II

This preprint was accepted September , 1999
Contact: A. I. Vinogradov

ABSTRACT:
This is the second part of the paper concerning the Riemann
hypothesis. The main theorem 2 is proved: every nontrivial
zero of the Riemann zeta function not lying on the critical
line is simultaneously a zero of all Dirichlet $L$-series
with quadratic characters.

From the main theorems of parts I and II, the Riemann
hypothesis is obtained for all Dirichlet $L$-series with
quadratic characters and for the Riemann zeta function.