One computational approach in support of the Riemann hypothesis

L. Aizenberg, V. Adamchik, V. E. Levit

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1 Scopus citations

Abstract

Some of the results on the criteria for the existence of an analytic continuation into a domain of a function given on a part of its boundary obtained by one of the authors are applied to the Riemann Hypothesis on the zeta-function zeroes. We include all of the basic structural information needed on the previous results on analytic continuation. Some comprehensive numerical experiments have been performed. We have found two important trends in the associated numerical results. The first one is that these findings favor the view that the Riemann Hypothesis is valid. The second one corresponds to a new conjecture on monotonic behavior of some sequences of integrals. The computational experiments have been performed with the Mathematics, V3.0.

Original languageEnglish
Pages (from-to)87-94
Number of pages8
JournalComputers and Mathematics with Applications
Volume37
Issue number1
DOIs
StatePublished - Jan 1999

Bibliographical note

Funding Information:
*The research of this author was supported in part by Binational Scientific Foundation Grant 94-00113.

Keywords

  • Analytic continuation of a function given on a part of its boundary
  • Computational experiments
  • Conformal mappings
  • Holomorphic functions
  • Riemann Hypothesis
  • Unit disk
  • ζ-function

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