Hilbert Modular Forms of Weight 1/2

Author: Achimescu, Sever

Year: 2005

Degree: Dissertation (Ph.D.)

Advisor: Ramakrishnan, Dinakar

Committee Members: Ramakrishnan, Dinakar; Wales, David B.; Flach, Matthias; Dunfield, Nathan M.

Option: Mathematics

DOI: 10.7907/PBNR-3X07

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

Let [...] be the space of Hilbert modular forms of half integral weight of all levels N and characters X.

We denote by φ_N : O_F → C a periodic function of period N.

Let Θ be the C-linear space of the functions f : H X H → C, [...] where, for each f,t ∈ O_F runs through a finite subset of totally positive integers of F.

Main Theorem.

H = Θ

Using this theorem, for some fixed F's, an explicit basis can be found. Some examples are given in Chapter 4.

Files

• abstract.pdf (application/pdf)
• ackno.pdf (application/pdf)
• ch1-5.pdf (application/pdf)
• contents.pdf (application/pdf)
• copyrightpage.pdf (application/pdf)
• titlepage.pdf (application/pdf)
• Achimescu-2005.pdf (application/pdf)