Generalized Volkenborn Integrals Associated with p -Adic Distributions and the Bernoulli Numbers

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Abstract

Abstract: Our goal is to give a formula representing the Bernoulli numbers by p-adic distributions. We consider p-adic distributions on the ring of p-adic integers which are invariant by rotations around the origin, and define a generalization of the Vokenborn integrals with respect to such distributions. It is shown the generalized Volkenborn integrals of power functions, and of negative powers of the p-adic norm converge under some conditions on the distributions, and their universal relation to the Bernoulli numbers is presented.

Original languageEnglish
Pages (from-to)164-171
Number of pages8
JournalP-Adic Numbers, Ultrametric Analysis, and Applications
Volume14
Issue number2
DOIs
Publication statusPublished - 2022 Jun

Keywords

  • $p$-adic distributions
  • Bernoulli numbers
  • Volkenborn integrals

ASJC Scopus subject areas

  • General Mathematics

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