an:05833556
Zbl 1211.11048
Hagemeier, Heike
Automorphic products of singular weight
DE
Mathematik. M??nchen: Dr. Hut; Darmstadt: TU Darmstadt, Fachbereich Mathematik (Diss.) (ISBN 978-3-86853-687-4/pbk). 136~p. (2010).
2010
b
11F11 11F41 11F55 11F27 11F30
orthogonal group; even lattice; vector valued modular form; vector valued Eisenstein series; Fourier coefficients; Borcherds product; singular weight; theta series
In this doctoral thesis the author constructs holomorphic modular forms of singular weight for the orthogonal group of an even lattice. For lattices of odd prime level she presents explicit formulas for the dimension of the spaces of vector valued modular forms (cusp forms) and for the Fourier coefficients of special vector valued Eisenstein series. She constructs lattices with trivial control space and determines the first Fourier coefficients of their Eisenstein series. On this way she finds a certain lattice, for which there exist Borcherds products of singular weight. She constructs one of these Borcherds products as a difference of two theta series.
Florin Nicolae (Berlin)