Zur Berechnung des Ranges der Schar der elliptischen Spitzenformen. (On the calculation of the dimension of the vector space of elliptic cusp forms)
Let \(\eta\) (q,g) denote the dimension of the vector space of elliptic cusp forms of integral weight g for the principal congruence subgroup of level q. The author applies the Selberg trace formula in order to compute \(\eta\) (q,g) including the cases \(g=1\) and \(g=2\). It is remarkable that, contrary to the case \(g\geq 3\), the hyperbolic elements give a contribution to the dimension integral if \(g=1,2\). The basic step is to derive the meromorphic continuation of the logarithmic derivative of a Selberg zeta function.
scientific article; zbMATH DE number 4160843
scientific article