Joint extreme values of the Riemann zeta function at harmonic points

TL;DR

This paper refines estimates for the joint extreme values of the Riemann zeta function at harmonic points using the resonance method, offering new insights and improvements over classical results.

Contribution

It introduces a refined approach employing the resonance method and Dirichlet series theory to better estimate extreme values of the zeta function at harmonic points.

Findings

Improved bounds for joint extreme values of the zeta function

Recovery of known extreme value results as corollaries

Enhanced understanding of the zeta function's behavior at harmonic points

Abstract

Using the resonance method, we obtain refined estimates for joint extreme values of the Riemann zeta function at harmonic points, improving upon Levinson's 1972 results and providing new insight into the behavior of the Riemann zeta function. Our proof is primarily based on Dirichlet series theory and the truncated Euler product for the Riemann zeta function. As a corollary, we can recover some previously known extreme value results for the zeta function.