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A note on zero density results implying large value estimates for Dirichlet polynomials

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arxiv 2403.13157 v1 pith:4MOFJSIK submitted 2024-03-19 math.NT

Kaisa Matomäki , Joni Teräväinen This is my paper · ORCID
classification math.NT
keywords estimatesdensitydirichletlargepolynomialsvaluezerofunction
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In this note we investigate connections between zero density estimates for the Riemann zeta function and large value estimates for Dirichlet polynomials. It is well known that estimates of the latter type imply estimates of the former type. Our goal is to show that there is an implication to the other direction as well, i.e. zero density estimates for the Riemann zeta function imply large value estimates for Dirichlet polynomials.

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  1. New exponent pairs, zero density estimates, and zero additive energy estimates: a systematic approach

    math.NT 2025-01 conditional novelty 6.0 of 10

    By systematically codifying and optimizing known exponent relations in the ANTEDB database, the paper derives four new exponent pairs, new zero density bounds, and new additive energy bounds for the Riemann zeta-function.

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