Addendum to ``On the scattering matrix of elliptic modular groups''
The author estimates the number of poles in the region \(0\leq\text{Re}(s)<{1\over 2}\), \(0<\text{Im}(s)\leq T\) of the determinant of the scattering matrix associated with the nonholomorphic Eisenstein series of weight \(g\) for the principal congruence subgroup of level \(q\) of the elliptic modular group. The asymptotic result is \[ {p(q)\over\pi}T\log T+c(q,g)T+O(\log T)\quad (T\to\infty) \] with certain constants \(p(q)\) and \(c(q,g)\). This improves his earlier result [Duke Math. J. 62, 479-509 (1991; Zbl 0729.11026)], where the error term was \(O(T)\).
scientific article; zbMATH DE number 58555