Explorations in the Theory of Partition Zeta Functions

Ken Ono (), Larry Rolen () and Robert Schneider ()
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Ken Ono: Emory University, Department of Mathematics and Computer Science
Larry Rolen: The Pennsylvania State University, Department of Mathematics
Robert Schneider: Emory University, Department of Mathematics and Computer Science

A chapter in Exploring the Riemann Zeta Function, 2017, pp 223-264 from Springer

Abstract: Abstract We introduce and survey results on two families of zeta functions connected to the multiplicative and additive theories of integer partitions. In the case of the multiplicative theory, we provide specialization formulas and results on the analytic continuations of these “partition zeta functions,” find unusual formulas for the Riemann zeta function, prove identities for multiple zeta values, and see that some of the formulas allow for p-adic interpolation. The second family we study was anticipated by Manin and makes use of modular forms, functions which are intimately related to integer partitions by universal polynomial recurrence relations. We survey recent work on these zeta polynomials, including the proof of their Riemann Hypothesis.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-59969-4_10

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DOI: 10.1007/978-3-319-59969-4_10

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