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

Trinh Khanh Duy

doi:10.1007/s10986-011-9143-3

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

Trinh Khanh Duy

Research Alliance Center for Mathematical Sciences (RACMaS)

Research output: Contribution to journal › Article › peer-review

4 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 language	English
Pages (from-to)	486-506
Number of pages	21
Journal	Lithuanian Mathematical Journal
Volume	51
Issue number	4
DOIs	https://doi.org/10.1007/s10986-011-9143-3
Publication status	Published - 2011 Sept

Keywords

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

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s10986-011-9143-3

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AB - 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.

KW - Fourier expansions

KW - Ramanujan expansions

KW - limit-periodic arithmetical function

KW - limit-periodic compactification

KW - multiplicative function

KW - ring of finite integral adeles

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JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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