Generalized Riemann hypotheses: sufficient and equivalent criteria

Abstract

This paper presents new sufficient and equivalent conditions for the generalized version of the Riemann Hypothesis. The paper derives also statements and remarks concerning zero-free regions, modified Hadamard-product formulas and the behaviour of $|\frac{L(\bar{\chi},s)}{L(\chi,1-s)}|$.Comment: Few changes. Accepted for publication in JP Journal of Algebra, Number Theory and Application