The moment zeta function and applications

2002/01/13 by Igor Rivin, Rivin, Igor
Chemistry · Mathematics · Physics and Astronomy · #11M06 #60C05 #60F99 #Advanced Physical and Chemical Molecular Interactions #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Graph theory and applications #Number Theory (math.NT) #Quantum Mechanics and Applications #math.CA #math.NT #msc:11M06 #msc:60C05 #msc:60F99

paper · pdf · doi:10.48550/arxiv.math/0201109

19 pages, supercedes a part of cs.LG/0107033

arxiv created 2002/01/13 · openalex publication_date 2002/01/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by a probabilistic analysis of a simple game (itself inspired by a problem in computational learning theory) we introduce the 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.

Related

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