Weighted Sylvester sums on the Frobenius set

2021/05/18 by Takao Komatsu, Yuan Zhang, Komatsu, Takao +1 · 1 citation
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2105.08274

openalex publication_date 2021/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let a and b be relatively prime positive integers. In this paper the weighted sum ∑_n∈\rm NR(a,b)λ^n-1n^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.

Citations

• A Linear Diophantine Problem

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• A Unified Approach to Calculating Sylvester Sums

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