Ternary universal sums of generalized polygonal numbers-Reference-Cited by-同舟云学术

Ternary universal sums of generalized polygonal numbers

Published:2019-04-29 Issue:04 Volume:15 Page:655-675
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Ju Jangwon¹,Oh Byeong-Kweon²,Seo Bangnam³

Affiliation:

1. Research Institute of Mathematics, Seoul National University, Seoul 08826, Korea

2. Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, Korea

3. Department of Mathematical Sciences, Seoul National University, Seoul 08826, Korea

Abstract

An integer of the form [Formula: see text], for some integer [Formula: see text], is called a generalized polygonal number of order [Formula: see text]. A ternary sum [Formula: see text] of generalized polygonal numbers, for some positive integers [Formula: see text] and some integers [Formula: see text], is said to be universal over [Formula: see text] if for any nonnegative integer [Formula: see text], the equation [Formula: see text] has an integer solution [Formula: see text]. In this paper, we prove the universalities of [Formula: see text] ternary sums of generalized polygonal numbers, which was conjectured by Sun.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042119500350

Reference12 articles.

1. On spinor exceptional representations

2. Spinor representations of positive definite ternary quadratic forms

3. Arithmetic of Quadratic Forms

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