### 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 |

### 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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## Cite this

Trinh, K. D. (2011). Limit-periodic arithmetical functions and the ring of finite integral adeles.

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