On variants of Chebyshev's conjecture

Fuente: arXiv
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Main Author: Suzuki, Masatoshi
Format: Preprint
Published: 2024
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author Suzuki, Masatoshi
author_facet Suzuki, Masatoshi
contents We show that the sign constancy for the values of certain weighted summatory functions of the von Mangoldt function implies the Riemann hypothesis or the generalized Riemann hypothesis for Dirichlet $L$-functions. While such sign constancy is challenging to establish individually, we prove that the summatory functions under study have constant signs on average.
format Preprint
id arxiv_https___arxiv_org_abs_2411_07436
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle On variants of Chebyshev's conjecture
Suzuki, Masatoshi
Number Theory
11M26, 11N05
We show that the sign constancy for the values of certain weighted summatory functions of the von Mangoldt function implies the Riemann hypothesis or the generalized Riemann hypothesis for Dirichlet $L$-functions. While such sign constancy is challenging to establish individually, we prove that the summatory functions under study have constant signs on average.
title On variants of Chebyshev's conjecture
topic Number Theory
11M26, 11N05
url https://arxiv.org/abs/2411.07436