Proof of generalized Riemann hypothesis for Dedekind zetas and Dirichlet L-functions

Abstract

A short proof of the generalized Riemann hypothesis (gRH in short) for zeta functions ${\zeta }_k$ of algebraic number fields $k$ - based on the Hecke's proof of the functional equation for ${\zeta }_k$ and the method of the proof of the Riemann hypothesis derived in [$M_A$] (algebraic proof of the Riemann hypothesis) is given. The generalized Riemann hypothesis for Dirichlet L-functions is an immediately consequence of (gRH) for ${\zeta }_k$ and suitable product formula which connects the Dedekind zetas with L-functions.

arXiv comment47 pages

References in corpus (1)

• A proof of the Riemann hypothesis