Semigroup's series for negative degrees of the gaps values in numerical semigroups generated by two integers and identities for the Hurwitz zeta functions

TL;DR

This paper derives an explicit inverse power series for the gaps in numerical semigroups generated by two integers, leading to new identities for the Hurwitz zeta function.

Contribution

It introduces a novel explicit series expression for gap values and establishes new identities for the Hurwitz zeta function.

Findings

Explicit inverse power series for gaps in two-generated numerical semigroups

New identities for the Hurwitz zeta function derived from the series

Enhanced understanding of the structure of numerical semigroup gaps

Abstract

We derive an explicit expression for an inverse power series over the gaps values of numerical semigroups generated by two integers. It implies a set of new identities for the Hurwitz zeta function.