Universal sums of generalized heptagonal numbers

被引：0

作者：

Kamaraj, Ramanujam ^{[1
]}

Kane, Ben ^{[1
]}

Oishi-Tomiyasu, Ryoko ^{[2
]}

机构：

[1] Univ Hong Kong, Dept Math, Pokfulam, Hong Kong, Peoples R China

[2] Kyushu Univ, Inst Math Ind, Kyushu, Japan

来源：

JOURNAL OF NUMBER THEORY | 2023年 / 249卷

关键词：

Diophantine equations; Sums of polygonal numbers; Theta functions; Quadratic forms; QUADRATIC-FORMS;

D O I：

10.1016/j.jnt.2023.02.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider representations of integers as sums of heptagonal numbers with a prescribed number of repeats of each heptagonal number appearing in the sum. In particular, we investigate the classification of such sums which are universal, i.e., those that represent every positive integer. We prove an explicit finite bound such that a given sum is universal if and only if it represents positive integer up to the given bound. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：500 / 536

页数：37

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