Integral Quadratic Forms Avoiding Arithmetic Progressions

2019/09/18 by Earnest, A. G., Kim, Ji Young
#11B25 11E12 11E20 (secondary) #11E25 (primary) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1909.08561

Abstract

For every positive integer k, it is shown that there exists a positive definite diagonal quaternary integral quadratic form that represents all positive integers except for precisely those which lie in k arithmetic progressions. For k=1, all forms with this property are determined.

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