Modular forms for the orthogonal group O(2,5)
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.
info:eu-repo/classification/ddc/510, Mathematik, Modulform, Orthogonale Gruppe, Borcherds-Produkt, Graduierter Ring, modular forms, orthogonal group, graded ring, borcherds products
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