论文标题
原发性对角线二次形式
Prime-universal diagonal quadratic forms
论文作者
论文摘要
如果代表所有素数，则据说（正确定和不可或缺的）二次形式为$ \ textit {prime-Universal} $。最近，Doyle和Williams在[2]中将所有原始的对角线三元二次形式归类为所有提议的猜想，并根据自己提出的两个猜想。在本文中，我们对所有主要的对角线二次形式进行了分类，而不论等级如何。此外，我们证明，所谓的$ 67 $ - 理论是对角线二次形式的主要宇宙。
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.
