Sum of three squares and class numbers of imaginary quadratic fields

Proceedings of the Japan Academy, Series A. Mathematical Sciences

article

Peter Jaehyun Cho¹ 

[1] Department of Mathematics, University of Toronto, Bahen Centre

关键词: Sum of three squares;    class number;    imaginary quadratic field;    arithmetic progression.;   

DOI  :  10.3792/pjaa.87.91

学科分类：数学（综合）

来源: Japan Academy

【 摘 要 】

For a positive integer $k$ and a certain arithmetic progression $A$, there exist infinitely many quadratic fields $\mathbf{Q}(\sqrt{-d})$ whose class numbers are divisible by $k$ and $d\in A$. From this, we have a linear congruence of the representation numbers of integers as sums of three squares.

【 授权许可】

Unknown