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

Khanh Duy Trinh

Research output: Contribution to journalArticle

3 Citations (Scopus)

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

Fingerprint

Arithmetical Function
Periodic Functions
Ring
Multiplicative Functions
Haar Measure
Additive Function
Fourier Expansion
Probability Space
Natural Extension
Random variable

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)

Cite this

Limit-periodic arithmetical functions and the ring of finite integral adeles. / Trinh, Khanh Duy.

In: Lithuanian Mathematical Journal, Vol. 51, No. 4, 01.09.2011, p. 486-506.

Research output: Contribution to journalArticle

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