Prime-universal diagonal quadratic forms
Number Theory
2020-06-29 v1
Abstract
A (positive definite and integral) quadratic form is said to be 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, -Theorem for a diagonal quadratic form to be prime-universal.
Cite
@article{arxiv.2006.14786,
title = {Prime-universal diagonal quadratic forms},
author = {Jangwon Ju and Daejun Kim and Kyoungmin Kim and Mingyu Kim and Byeong-Kweon Oh},
journal= {arXiv preprint arXiv:2006.14786},
year = {2020}
}
Comments
14 pages