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Limit-periodic arithmetical functions and the ring of finite integral adeles |
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| Authors: | Trinh?Khanh?Duy mailto:khanhduy@gmail.com" title=" khanhduy@gmail.com" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
| Affiliation: | 1.Department of Mathematics, Graduate School of Science,Osaka University,Osaka,Japan |
| 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. |
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