Quadratic forms with a strong regularity property on the representations of squares

2019/09/04 by Kyoungmin Kim, Byeong-Kweon Oh, Kim, Kyoungmin +1
Mathematics · #11E12 #11E20 #Advanced Algebra and Geometry #Analytic Number Theory Research #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1909.01833

openalex publication_date 2019/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A (positive definite and non-classic integral) quadratic form is called strongly s-regular if it satisfies a strong regularity property on the number of representations of squares of integers. In this article, we prove that for any integer k ≥ 2, there are only finitely many isometry classes of strongly s-regular quadratic forms with rank k if the minimum of the nonzero squares that are represented by them is fixed.

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