Limit-periodic arithmetical functions and the ring of finite integral adeles |
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Authors: | Email author" target="_blank">Trinh?Khanh?DuyEmail author |
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Institution: | 1.Department of Mathematics, Graduate School of Science,Osaka University,Osaka,Japan |
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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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Keywords: | |
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