Algebra and Arithmetic of Modular Forms

Abstract

I will present my PhD thesis, focusing on the topic of graded rings of modular forms. For such rings, I will determine bounds of the weights of modular forms constituting a minimal set of generators, as well as on the degree of the generators of the ideal of relations between them. I will formulate conjectures on the minimal generating weight for modularforms with coecients in Z. I will also discuss some results related to the theory of modular forms modulo prime powers.

Principal supervisor: Prof. Ian Kiming, Math, Copenhagen

Assessment committee:

Chairman: Lars H. Halle, Math. Copenhagen

Prof. Carel Faber,  KTH, Sweden

Ass Prof. John Voight, Dartmouth College, USA