Detecting zeros of Dirichlet L-functions via the Riemann zeta-function

2025/08/25 by Suzuki, Masatoshi
#11M26 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.17701

Abstract

Assuming the Riemann hypothesis, we show that a certain vertical distribution of the nontrivial zeros of the Riemann zeta-function is equivalent to the generalized Riemann hypothesis for Dirichlet L-functions. Furthermore, under both the Riemann hypothesis and the generalized Riemann hypothesis, we show that the nontrivial zeros of Dirichlet L-functions can be detected through those of the Riemann zeta-function.

Citations

• On variants of Chebyshev's conjecture
• The Generalized Riemann Hypothesis from zeros of a single L-function
• The Generalized Riemann Hypothesis from zeros of the zeta function
• Towards the Generalized Riemann Hypothesis using only zeros of the Riemann zeta function
• Moments of the Riemann zeta-function

Related

• The Riemann Hypothesis for Dirichlet L Functions
• The Generalized Riemann Hypothesis from zeros of the zeta function
• The positivity technique and low-lying zeros of Dirichlet L-functions
• The positivity technique and low-lying zeros of Dirichlet L-functions
• On the Riemann Hypothesis and its generalizations