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

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 -functions on the level of the Bondarenko–Seip bound.

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Bibliographic Details
Main Authors: Bondarenko, Andrii, Darbar, Pranendu, Hagen, Markus Valås, Heap, Paul Winston, Seip, Kristian
Format: Article
Language:English
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Summary: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 -functions on the level of the Bondarenko–Seip bound.
ISSN:2963-2975