Representations of the Riemann zeta function: A probabilistic approach

Jiamei Liu; Yuxia Huang; Chuancun Yin

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arXiv · 1901.11183

Representations of the Riemann zeta function: A probabilistic approach

Jiamei Liu·Yuxia Huang·Chuancun Yin

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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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Jiamei Liu, Yuxia Huang, Chuancun Yin. 2019-01-31. Representations of the Riemann zeta function: A probabilistic approach. https://arxiv.org/abs/1901.11183

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