Prime-universal diagonal quadratic forms

2020/06/26 by Ju, Jangwon, Kim, Daejun, Kim, Kyoungmin +2
#11E12 #11E20 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.14786

Abstract

A (positive definite and integral) quadratic form is said to be prime-universal if it represents all primes. Recently, Doyle and Williams in [2] classified all prime-universal diagonal ternary quadratic forms, and all prime-universal diagonal quaternary quadratic forms under two conjectures proposed by themselves. In this article, we classify all prime-universal diagonal quadratic forms regardless of ranks. Furthermore, we prove, so called, 67-Theorem for a diagonal quadratic form to be prime-universal.

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