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

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arxiv 1705.09921 v1 pith:2EN6I7RN submitted 2017-05-28 math.CA

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

Helmut Maier , Michael Th. Rassias This is my paper
classification math.CA
keywords sumscontainingcriterionestimateestimatesfunctionhypothesisnyman-beurling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We give an estimate for sums appearing in the Nyman-Beurling criterion for the Riemann Hypothesis containing the M\"obius function. The estimate is remarkably sharp in comparison to estimates of other sums containing the M\"obius function. The methods intensively use tools from the theory of continued fractions and from the theory of Fourier series.

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Cited by 2 Pith papers

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  1. A few remarks on the Baez-Duarte Criterion

    math.NT 2026-07 conditional novelty 6.0

    A canonical third-order truncation of a Vasyunin cotangent sum reduces the open boundedness problem in the Baez-Duarte criterion to an explicit bilinear cancellation estimate.

  2. A few remarks on the Baez-Duarte Criterion

    math.NT 2026-07 unverdicted novelty 3.0

    Several lemmas related to the Báez-Duarte criterion for the Riemann Hypothesis are claimed to be derived.