Analysis and combinatorics of partition zeta functions

Robert Schneider, Andrew V. Sills

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We examine "partition zeta functions"analogous to the Riemann zeta function but summed over subsets of integer partitions. We prove an explicit formula for a family of partition zeta functions already shown to have nice properties - those summed over partitions of fixed length - which yields complete information about analytic continuation, poles and trivial roots of the zeta functions in the family. Then we present a combinatorial proof of the explicit formula, which shows it to be a zeta function analog of MacMahon's partial fraction decomposition of the generating function for partitions of fixed length.

Original languageEnglish
Pages (from-to)805-814
Number of pages10
JournalInternational Journal of Number Theory
Volume17
Issue number3
DOIs
StatePublished - Apr 2021

Keywords

  • Integer partitions
  • MacMahon decomposition
  • partition zeta functions
  • zeta functions

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