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

2007/06/02 by Andrzej Mcadrecki, Mcadrecki, Andrzej
Mathematics · #11M26 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #General Mathematics (math.GM)

paper · pdf · doi:10.48550/arxiv.0706.0256

openalex publication_date 2007/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

A short proof of the generalized Riemann hypothesis (gRH in short) for zeta functions ζ_k of algebraic number fields k - based on the Hecke's proof of the functional equation for ζ_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 ζ_k and suitable product formula which connects the Dedekind zetas with L-functions.

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