The Laplacian On Hyperbolic Riemann Surfaces And Maass Forms
This thesis concerns the spectral theory of the Laplacian on Riemann surfaces of finite type, with emphasis on the quotients of the upper half plane by congruence subgroups. In a first part we show, following Otal, that on a Riemann surface M of genus g with n punctures there are at most 2g [-] 2 + n eigenvalues [lamda] with [lamda] [LESS-THAN OR EQUAL TO] 1/4. In a second part, we focus on arithmetic surfaces. This subject is treated by Maass in a paper that is difficult to read. We work out some examples of his construction of Maass forms.
Laplacian; Rieamann surfaces; Maass forms
Muscalu,Florin Camil; Saloff-Coste,Laurent Pascal; Ramakrishna,Ravi Kumar
Ph. D., Mathematics
Doctor of Philosophy
dissertation or thesis