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Asymptotic behaviors of convolution powers of the Riemann zeta distribution

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Abstract

In probability theory, there are discrete and continuous distributions. Generally speaking, we do not have sufficient kinds and properties of discrete ones compared to the continuous ones. In this paper, we treat the Riemann zeta distribution as a representative of few known discrete distributions with infinite supports. We discuss some asymptotic behaviors of convolution powers of the Riemann zeta distribution.

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Authors and Affiliations

  1. Department of Applied Mathematics, Faculty of Science, Okayama University of Science, 1-1, Ridaicho, Kita-ku, Okayama, 700-0005, Japan

    Takahiro Aoyama

  2. Department of Mathematics, Faculty of Education, Shizuoka University, 836, Ohya, Suruga-ku, Shizuoka, 422-8529, Japan

    Ryuya Namba

  3. Agile Solution Department, Smart Solution Division, Resona Digital I Inc., 2-13, Shinsenri-Nishimachi 1-chome, Toyonaka, Osaka, 560-0083, Japan

    Koki Ota

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  1. Takahiro Aoyama
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  2. Ryuya Namba
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  3. Koki Ota
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Correspondence to Ryuya Namba.

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Ryuya Namba is supported by JSPS KAKENHI grant No. 19K23410.

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Aoyama, T., Namba, R. & Ota, K. Asymptotic behaviors of convolution powers of the Riemann zeta distribution. Lith Math J 63, 1–12 (2023). https://doi.org/10.1007/s10986-023-09585-0

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  • DOI: https://doi.org/10.1007/s10986-023-09585-0

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