International Seminar on Automorphic Forms

Leila Smajlovic (University of Sarajevo): On an extension of the Rohrlich-Jensen formula

We revisit the Rohrlich-Jensen formula and prove that, in the case of any Fuchsian group of the first kind with one cusp it can be viewed as a regularized inner product of special values of two Poincaré series, one of which is the Niebur-Poincaré series and the other is the resolvent kernel of the Laplacian. The regularized inner product can be seen as a type of Maass-Selberg relation. In this form, we develop a Rohrlich-Jensen formula associated to any Fuchsian group Γ of the first kind with one cusp by employing a type of Kronecker limit formula associated to the resolvent kernel. We present two examples of our main result: First, when Γ is the full modular group; and second when Γ is an Atkin-Lehner group Γ0(N)+. This work is joint with James Cogdell and Jay Jorgenson.

https://tu-darmstadt.zoom.us/j/68048280736

The password is the first Fourier coefficient of the modular j-function (as digits)