对非对角秩为3的八个素变量二次型解的计数
Counting solutions to quadratic forms in eight prime variables of off-diagonal rank $3$
- University of Oxford（牛津大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文延续前人对素变量二次型解的计数研究，针对非对角秩为3的八个素变量非退化二次型，开展解的数量计数工作。
AI中文摘要：
本文计数非对角秩为3的八个素变量非退化二次型的解的数量。该研究是对前人工作的延续：L. Zhao计数了至少九个变量的二次型解；B. Green计数了八个变量的“一般”（隐含非对角秩为4）二次型解；J. Dobrowolski计数了八个变量且非对角秩至多为2的二次型解。
英文摘要：
In this note we count the number of solutions to a non-degenerate quadratic form in eight prime variables of off-diagonal rank $3$. It is a continuation of work by L. Zhao, who counted solutions to forms in at least nine variables, by B. Green, who counted solutions to 'generic' (which implies off-diagonal rank $4$) forms in eight variables, and by J. Dobrowolski, who counted solutions to forms in eight variables of off-diagonal rank at most $2$.
