### 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 |
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Pages (from-to) | 486-506 |

Number of pages | 21 |

Journal | Lithuanian Mathematical Journal |

Volume | 51 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2011 Sep 1 |

Externally published | Yes |

### Fingerprint

### 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

*Lithuanian Mathematical Journal*,

*51*(4), 486-506. https://doi.org/10.1007/s10986-011-9143-3

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

Research output: Contribution to journal › Article

*Lithuanian Mathematical Journal*, vol. 51, no. 4, pp. 486-506. https://doi.org/10.1007/s10986-011-9143-3

}

TY - JOUR

T1 - Limit-periodic arithmetical functions and the ring of finite integral adeles

AU - Trinh, Khanh Duy

PY - 2011/9/1

Y1 - 2011/9/1

N2 - 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.

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 - limit-periodic arithmetical function

KW - limit-periodic compactification

KW - multiplicative function

KW - Ramanujan expansions

KW - ring of finite integral adeles

UR - http://www.scopus.com/inward/record.url?scp=83355169570&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=83355169570&partnerID=8YFLogxK

U2 - 10.1007/s10986-011-9143-3

DO - 10.1007/s10986-011-9143-3

M3 - Article

AN - SCOPUS:83355169570

VL - 51

SP - 486

EP - 506

JO - Lithuanian Mathematical Journal

JF - Lithuanian Mathematical Journal

SN - 0363-1672

IS - 4

ER -