Preprint Hypothesis Version 1 Preserved in Portico This version is not peer-reviewed

# On the Distribution of the Nontrivial Zeros for the Dirichlet L-Functions

Version 1 : Received: 3 May 2021 / Approved: 6 May 2021 / Online: 6 May 2021 (11:30:06 CEST)

How to cite: Yang, X. On the Distribution of the Nontrivial Zeros for the Dirichlet L-Functions. Preprints 2021, 2021050072 (doi: 10.20944/preprints202105.0072.v1). Yang, X. On the Distribution of the Nontrivial Zeros for the Dirichlet L-Functions. Preprints 2021, 2021050072 (doi: 10.20944/preprints202105.0072.v1).

## Abstract

This paper addresses a variant of the product for the Dirichlet $L$--functions. We propose a completely detailed proof for the truth of the generalized Riemann conjecture for the Dirichlet $L$--functions, which states that the real part of the nontrivial zeros is $1/2$. The Wang and Hardy--Littlewood theorems are also discussed with removing the need for it. The results are applicable to show the truth of the Goldbach's conjecture.

## Keywords

Dirichlet L-function; generalized Riemann conjecture; nontrivial zeros; Goldbach's conjecture; Riemann zeta function

## Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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