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 language | English |
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Pages (from-to) | 805-814 |
Number of pages | 10 |
Journal | International Journal of Number Theory |
Volume | 17 |
Issue number | 3 |
DOIs | |
State | Published - Apr 2021 |
Keywords
- Integer partitions
- MacMahon decomposition
- partition zeta functions
- zeta functions