UVM Theses and Dissertations
Format:
Print
Author:
Klug, Michael R.
Dept./Program:
Mathematics
Year:
2013
Degree:
MS
Abstract:
The classical theory of modular forms for the group SL₂ (Z) has been applied fruitfully throughout mathematics, particularly in number theory. Following the method of Voight and Willis, we develop power series techniques to explicitly compute rings of modular forms for cocompact Fuchsian groups arising from quaternion algebras. These rings are computed by exhibiting sets of generators and relations. We also develop a technique for normalizing modular forms in such a way that the power series coefficients are integers.