Limit-periodic arithmetical functions and the ring of finite integral adeles

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Abstract

In this paper, we show that the ring of finite integral adeles, together with its Borel field and its normalized Haar measure, is an appropriate probability space where limit-periodic arithmetical functions can be extended to random variables. The natural extensions of additive and multiplicative functions are studied. Besides, the convergence of Fourier expansions of limit-periodic functions is proved.

Original languageEnglish
Pages (from-to)486-506
Number of pages21
JournalLithuanian Mathematical Journal
Volume51
Issue number4
DOIs
Publication statusPublished - 2011 Sep 1
Externally publishedYes

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Keywords

  • Fourier expansions
  • limit-periodic arithmetical function
  • limit-periodic compactification
  • multiplicative function
  • Ramanujan expansions
  • ring of finite integral adeles

ASJC Scopus subject areas

  • Mathematics(all)

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