Hilbert Modular Forms of Weight 1/2

Citation

Achimescu, Sever (2005) Hilbert Modular Forms of Weight 1/2. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/PBNR-3X07. https://resolver.caltech.edu/CaltechETD:etd-04272005-172254

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.

Thesis Files