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

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          Abstract

          We give a conditional result on the constant in the B\'aez-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.

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          Journal
          2012-11-21
          Article
          10.1134/S0081543813030036
          1211.5191
          5b01d67a-2a5f-466d-923f-4cde0ba49f49

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
          Custom metadata
          11M26
          Mathematics and Informatics, 1, Dedicated to 75th Anniversary of Anatolii Alekseevich Karatsuba, Sovrem. Probl. Mat., 16, Steklov Math. Inst., 2012, 38-44
          9 pages
          math.NT

          Number theory
          Number theory

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