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Partition zeta functions

Research in Number Theory20162:9

https://doi.org/10.1007/s40993-016-0039-5

  • Received: 14 August 2015
  • Accepted: 11 February 2016
  • Published:

Abstract

We exploit transformations relating generalized q-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as π, and to connect sums over partitions to the Riemann zeta function, multiple zeta values, and other number-theoretic objects.

Keywords

  • Partitions
  • q-series
  • Zeta functions

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