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The moment zeta function and applications

Igor Rivin
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Abstract

Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the \emph{moment zeta function} of a probability distribution, and study in depth some asymptotic properties of the moment zeta function of those distributions supported in the interval [0, 1]. One example of such zeta functions is Riemann's zeta function (which is the moment zeta function of the uniform distribution in [0, 1]. For Riemann's zeta function we are able to show particularly sharp versions of our results.

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Igor Rivin. 2002-01-13. The moment zeta function and applications. https://arxiv.org/abs/math/0201109

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