Representations of the Riemann zeta function: A probabilistic approach

2019/01/31 by Jiamei Liu, Liu, Jiamei, Yuxia Huang +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Approximation and Integration #Probability (math.PR) #Statistical Mechanics and Entropy #math.PR

paper · pdf · doi:10.48550/arxiv.1901.11183

arxiv created 2019/01/31 · openalex publication_date 2019/01/31 · arxiv updated 2019/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we give a short elementary proof of the well known Euler's recurrence formula for the Riemann zeta function at positive even integers and integral representations of the Riemann zeta function at positive integers and at fractional points by means of probabilistic approach. The proof is based on the moment generating function and the characteristic function of logistic and half-logistic distributions in probability theory.

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