Riemann Hypothesis: On Closed Sets of Equations for the Trend, the Tiny and Complete Li-Keiper Coefficients

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Authors: Danilo Merlini, Luca Rusconi, Massimo Sala, and Nicoletta Sala
Page Range: 3-25
Published in: Chaos and Complexity Letters, 16#1 (2022)
ISSN: 1556-3995

ISBN: N/A Category:

Table of Contents

ABSTRACT

In connection with the binomial transform, we establish a concrete asymptotic expression for the (trend, tiny part and complete) Li-Keiper coefficients in terms of elementary functions. The tiny fluctuations are computed up to n=5000 and a careful numerical analysis allows the derivation of an asymptotic formula using the extreme values of such fluctuations which is correct up to n=100000. Such an asymptotic expression – do not assume – but it is in agreement with the assumption of the truth of the Riemann Hypothesis.

Keywords: Li-Keiper coefficients, tiny part, approximations, numerical experiments, Riemann Hypothesis.