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arXiv · 2006.14786

Prime-universal diagonal quadratic forms

Jangwon Ju·Daejun Kim·Kyoungmin Kim·Mingyu Kim·Byeong-Kweon Oh
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Abstract

A (positive definite and integral) quadratic form is said to be $\textit{prime-universal}$ 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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Jangwon Ju, Daejun Kim, Kyoungmin Kim, Mingyu Kim, Byeong-Kweon Oh. 2020-06-26. Prime-universal diagonal quadratic forms. https://arxiv.org/abs/2006.14786

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