On the exceptional sets of integral quadratic forms

2020/03/25 by Chan, Wai Kiu, Oh, Byeong-Kweon
#11E12 #11E25 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2003.11322

Abstract

A collection \mathcal S of equivalence classes of positive definite integral quadratic forms in n variables is called an n-exceptional set if there exists a positive definite integral quadratic form which represents all equivalence classes of positive definite integral quadratic forms in n variables except those in \mathcal S. We show that, among other results, for any given positive integers m and n, there is always an n-exceptional set of size m and there are only finitely many of them.

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