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.
Mathematics Subject Classification (2010): 60E07, 60F15, 60J20, 91E40, 26C10
Mathematics Subject Classification (2010):60E07, 60F15, 60J20, 91E40, 26C10
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Acknowledgements
The author would like to thank the EPSRC,the NSF, and the Berlin Mathematics School for support, Technische Universität Berlin for its hospitality during the revision of this paper and Natalia Komarova Ilan Vardi, and Jeff Lagarias for useful conversations. Lagarias, in particular, has pointed out the connection of this work to Li’s work on the Riemann hypothesis, see [2, 5, 6].
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Rivin, I. (2013). The Moment Zeta Function and Applications. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_22
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DOI: https://doi.org/10.1007/978-1-4614-4075-8_22
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