Local Newforms for SL(2, F) Over Non-Archimedean Fields

This book was the result of two years of research I conducted with Brooks Roberts at the University of Idaho. When I began graduate school at the University of California Santa Cruz, my advisor was Ehud Moshe Baruch, who also specialized in automorphic representations. Studying with Brooks allowed me to complete the research I had started years earlier in California. This work is a modest addition to what is called the Langland's Program to connect the worlds of algebraic curves, Galois representations, and automorphic representations via their associated L-functions. In particular, we can use these types of representations to build representations of adeles (see Weil's Basic Number Theory).