On the distribution of the eigenvalues of the hyperbolic Laplacian for PSL\((2,\mathbb{Z})\). II. (Q5929407)

We maintain the notation of the review of Part I [see Math. Z. 234, 241--254 (2000; Zbl 1026.11051)]. It is the aim of Part II to show that the numbers \(2t_j\log (t_j/\pi e)\) \((j\geq 1)\) are not well distributed mod\,1. This is due to the fact that the norms of the hyperbolic elements of \(\text{SL}_2 (\mathbb{Z})\) are very close to being squares of integers.