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On further application of the zeta distribution to number theory

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Abstract

This note gives some applications of the zeta distribution to number theory. First, a number of probabilistic proofs of the equality between the Riemann zeta functions and some number-theoretic functions are provided. Second, some problems of probability with respect to positive integers considered in the literature are discussed in the zeta distribution case. In contrast to usual heuristic arguments of probabilistic approach in number theory where the uniform distribution is assumed on positive integers, the proofs here are rigorous by utilizing the zeta distributions on positive integers.

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Correspondence to Naohiro Yoshida.

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Fujita, T., Yoshida, N. On further application of the zeta distribution to number theory. Res. number theory 9, 81 (2023). https://doi.org/10.1007/s40993-023-00485-3

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