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arXiv · 2105.08274

Weighted Sylvester sums on the Frobenius set

Takao Komatsu·Yuan Zhang
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Abstract

Let $a$ and $b$ be relatively prime positive integers. In this paper the weighted sum $\sum_{n\in{\rm NR}(a,b)}\lambda^{n-1}n^m$ is given explicitly or in terms of the Apostol-Bernoulli numbers, where $m$ is a nonnegative integer, and ${\rm NR}(a,b)$ denotes the set of positive integers nonrepresentable in terms of $a$ and $b$.

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Takao Komatsu, Yuan Zhang. 2021-05-18. Weighted Sylvester sums on the Frobenius set. https://arxiv.org/abs/2105.08274

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