Arithmetical Aspects of Beurling's Real Variable Reformulation of the Riemann Hypothesis

2000/11/29 by Luis Baez-Duarte, Baez-Duarte, Luis
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0011254

21 pages

arxiv created 2000/11/29 · arxiv updated 2009/11/30

Abstract

The paper presents two arithmetical versions of the Nyman-Beurling equivalence with the Riemann hypothesis, proved by classical, quasi elementary, number-theoretic methods, based on an integrated version of the classical combinatorial identity for Moebius numbers. These proofs also give insight into the troublesome phenomenon that many natural sequences of Beurling functions tending to the indicator function of (0,1) both pointwise and in L1 norm do not converge in L2 norm.

Related

• Estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis
• Explicit estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis
• Cotangent sums related to the Riemann Hypothesis for various shifts of the argument
• Densities, Laplace Transforms and Analytic Number Theory
• Proof of the Riemann's hypothesis