Modular forms for the orthogonal group O(2,5)
type: CreativeWork
description: This thesis deals with modular forms for orthogonal groups of signature (2,n), n>2, with particular emphasis on the case n=5. First we determine suitable generators and the abelian characters of some orthogonal groups. Then we present a few methods for constructing orthogonal modular forms: by means of a differential operator of Rankin-Cohen type, as Maass' lifts of Jacobi forms, as modular forms for symplectic groups of degree 2, as invariant polynomials of theta series, and as Borcherds products. The Borcherds products are (meromorphic) modular forms with explicitly known divisors. Using a reduction process we can, in two cases, determine generators of the graded ring of orthogonal modular forms. It turns out that in both cases the graded ring of modular forms of even weight with respect to the trivial character is a polynomial ring in six (algebraically independent) generators.
abstract: This thesis deals with modular forms for orthogonal groups of signature (2,n), n>2, with particular emphasis on the case n=5. First we determine suitable generators and the abelian characters of some orthogonal groups. Then we present a few methods for constructing orthogonal modular forms: by means of a differential operator of Rankin-Cohen type, as Maass' lifts of Jacobi forms, as modular forms for symplectic groups of degree 2, as invariant polynomials of theta series, and as Borcherds products. The Borcherds products are (meromorphic) modular forms with explicitly known divisors. Using a reduction process we can, in two cases, determine generators of the graded ring of orthogonal modular forms. It turns out that in both cases the graded ring of modular forms of even weight with respect to the trivial character is a polynomial ring in six (algebraically independent) generators.
author: Klöcker, Ingo Herbert
language: eng
keywords: info:eu-repo/classification/ddc/510, Mathematik, Modulform, Orthogonale Gruppe, Borcherds-Produkt, Graduierter Ring, modular forms, orthogonal group, graded ring, borcherds products
date published: 2006
date modified: 2026-07-30T19:43:02Z
provider: RWTH Aachen University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Publikationsserver der RWTH Aachen University