2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63104Motivated 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.19 pages, supercedes a part of cs.LG/0107033Number TheoryClassical Analysis and ODEs11M06; 60F99; 60C05text