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arXiv · 2302.08285

A dichotomy for extreme values of zeta and Dirichlet L-functions

Andriy Bondarenko·Pranendu Darbar·Markus Valås Hagen·Winston Heap·Kristian Seip
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Abstract

We exhibit large values of the Dedekind zeta function of a cyclotomic field on the critical line. This implies a dichotomy whereby one either has improved lower bounds for the maximum of the Riemann zeta function, or large values of Dirichlet $L$-functions on the level of the Bondarenko--Seip bound.

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Andriy Bondarenko, Pranendu Darbar, Markus Valås Hagen, Winston Heap, Kristian Seip. 2023-02-16. A dichotomy for extreme values of zeta and Dirichlet L-functions. https://doi.org/10.1112/blms.12904

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