On Sylvester sums of compound sequence semigroup complements

Abstract

In this paper, we consider the set $\text{NR}(G)$ of natural numbers which are not in the numerical semigroup generated by a compound sequence $G$. We generalize a result of Tuenter which completely characterizes $\text{NR}(G)$. We use this result to compute Sylvester sums, and we give a direct application to the computation of weights of higher-order Weierstrass points on some families of complex algebraic curves.

17 pages, revised, originally submitted for publication December '16

References in corpus (3)

• Numerical semigroups on compound sequences
• Weierstrass points of superelliptic curves
• Higher-order Weierstrass weights of branch points on superelliptic curves

Cited by in corpus (1)

• Equidistribution Conditions for Gaps of Geometric Numerical Semigroups