Open Access

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: 15 March 2016

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