The moment zeta function and applications
Number Theory
2007-05-23 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.math/0201109,
title = {The moment zeta function and applications},
author = {Igor Rivin},
journal= {arXiv preprint arXiv:math/0201109},
year = {2007}
}
Comments
19 pages, supercedes a part of cs.LG/0107033