Counting modular matrices with specified Euclidean norm
Let N(x) be the number of matrices \(\left( \begin{matrix} a\\ c\end{matrix} \begin{matrix} b\\ d\end{matrix} \right)\in SL(2,{\mathbb{Z}})\) whose Euclidean norm \(a^ 2+b^ 2+c^ 2+d^ 2\) does not exceed x. Then \(\lim_{x\to \infty}N(x)/x=6\).
scientific article; zbMATH DE number 4047810