An optimal choice of Dirichlet polynomials for the Nyman-Beurling criterion

We give a conditional result on the constant in the Báez-Duarte reformulation of the Nyman-Beurling criterion for the Riemann Hypothesis. We show that assuming the Riemann hypothesis and that \(\sum_{\rho}\frac{1}{|\zeta'(\rho)|^2}\ll T^{3/2-\delta}\), for some \(\delta>0\), the value of thi...

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Bibliographic Details
Published in:arXiv.org 2012-11
Main Authors: Bettin, Sandro, Conrey, J Brian, Farmer, David W
Format: Article
Language:English
Subjects:
Criteria
Dirichlet problem
Hypotheses
Lower bounds
Polynomials
Online Access:Get full text
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Summary:We give a conditional result on the constant in the Báez-Duarte reformulation of the Nyman-Beurling criterion for the Riemann Hypothesis. We show that assuming the Riemann hypothesis and that \(\sum_{\rho}\frac{1}{|\zeta'(\rho)|^2}\ll T^{3/2-\delta}\), for some \(\delta>0\), the value of this constant coincides with the lower bound given by Burnol.
ISSN:2331-8422
DOI:10.48550/arxiv.1211.5191