Computation of Eisenstein series associated with discriminant forms
In this thesis, we describe methods to compute the Fourier coefficients of Eisenstein series for the Weil representation associated to an even lattice. The known formulas depend on an even lattice and use the "local" data derived from this lattice. A python program for use within sage was...
| Main Author: | |
|---|---|
| Format: | Others |
| Language: | en |
| Published: |
2018
|
| Online Access: | http://tuprints.ulb.tu-darmstadt.de/8261/1/20181203_Dissertation_Sebastian_Opitz.pdf Opitz, Sebastian <http://tuprints.ulb.tu-darmstadt.de/view/person/Opitz=3ASebastian=3A=3A.html> : Computation of Eisenstein series associated with discriminant forms. Technische Universität, Darmstadt [Ph.D. Thesis], (2018) |
| Summary: | In this thesis, we describe methods to compute the Fourier coefficients of Eisenstein series for the Weil representation associated to an even lattice. The known formulas depend on an even lattice and use the "local" data derived from this lattice. A python program for use within sage was written to evaluate these formulas. The Eisenstein series itself only depends on the discriminant form of the lattice, and hence depends only on the "local" data. We examine the "global" formulas to see how they can be computed purely from "local" data, which can be encoded by a genus symbol or a Jordan decomposition. A comparison of two different approaches to the computation of the Fourier coefficients leads to formulas for the Igusa local zeta function. At last we use the implemented programs to classify all Borcherds products coming from a certain class of lattices. |
|---|