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arXiv · 1612.04766

On Sylvester sums of compound sequence semigroup complements

Thomas A. Gassert·Caleb M. Shor
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Abstract

In this paper, we consider the set $\textit{NR}(G)$ 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 $\textit{NR}(G)$. 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.

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Thomas A. Gassert, Caleb M. Shor. 2017-03-29. On Sylvester sums of compound sequence semigroup complements. https://doi.org/10.1016/j.jnt.2017.03.025

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