Extreme values of zeta and L-functions

TL;DR

This paper introduces a resonance method to generate large and small values of the Riemann zeta function and L-functions at critical points, advancing understanding of their extreme behaviors.

Contribution

The paper presents a novel resonance technique for constructing extreme values of zeta and L-functions, providing new tools for their analysis.

Findings

Successfully produces large zeta values using the resonance method

Generates both large and small central values of L-functions

Enhances understanding of the extremal behavior of zeta and L-functions

Abstract

We introduce a "resonance" method to produce large values of $|\zeta(1/2+it)|$ and large and small central values of $L$-functions.