Estimates of sums related to the Nyman-Beurling criterion for the Riemann Hypothesis

2017/05/28 by Helmut Maier, Maier, Helmut, Michael Th. Rassias +1
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1705.09921

Abstract

We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis containing the Möbius function. The estimate is remarkably sharp in comparison to estimates of other sums containing the Möbius function. The methods intensively use tools from the theory of continued fractions and from the theory of Fourier series.

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