Sums of generalized polygonal numbers of almost prime "length"

2024/09/12 by Soumyarup Banerjee, Ben Kane, Banerjee, Soumyarup +3
Mathematics · #11E20 #11E45 #11F27 #11F37 #11N36 #Algebraic and Geometric Analysis #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2409.07895

openalex publication_date 2024/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider sums of three generalized m-gonal numbers whose parameters are restricted to integers with a bounded number of prime divisors. With some restrictions on m modulo 30, we show that a density one set of integers is represented as such a sum, where the parameters are restricted to have at most 6361 prime factors. Moreover, if the squarefree part of f_m(n) is sufficiently large, then n is represented as such a sum, where f_m(n) is a natural linear function in n.

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