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. Preprints2021, 2021050072. https://doi.org/10.20944/preprints202105.0072.v1.
Yang, X. On the Distribution of the Nontrivial Zeros for the Dirichlet L-Functions. Preprints 2021, 2021050072. https://doi.org/10.20944/preprints202105.0072.v1.
Cite as:
Yang, X. On the Distribution of the Nontrivial Zeros for the Dirichlet L-Functions. Preprints2021, 2021050072. https://doi.org/10.20944/preprints202105.0072.v1.
Yang, X. On the Distribution of the Nontrivial Zeros for the Dirichlet L-Functions. Preprints 2021, 2021050072. https://doi.org/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.
MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
