TY  - GEN
TI  - Construction of Harmonic Maass Forms in
Small Weight
Y1  - 2017///
ID  - heidok22981
A1  - Rohloff, Marc
N2  - This thesis deals with various problems regarding  automorphic forms of small weight. We study the continuation of Poincaré and Eisenstein series, as well as more abstract construction principles for harmonic Maass forms. Further, we show by using Riemann-Roch that the automorphic forms we constructed provide us with a basis for the weakly harmonic
Maass forms. The difficulties encountered are solved by the introduction of a new type of vector space for square integrable automorphic forms, the Petersson-Sobolev spaces, which are defined in analogy to functional analytic Sobolev spaces. We show that these spaces provide us with a notion of invertibility of the Laplace operator as well as regularity theorems for the Petersson-Sobolev spaces, which are similar to the Sobolev imbedding theorems of functional analysis. The properties of the Petersson-Sobolev spaces then provide us with the tools required to solve the problems studied.
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/22981/
AV  - public
ER  -