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