This Course is Independent of Last Semesters Course

 
Summary: This semester I want to begin by discussing the Selberg Property Tau as well as his "1/4" Eigenvalue Conjecture.  This will involve some graph theory.  We will consider certain expander graphs constructed by A. Terras et al and eventually derive Tau from them, resulting in further applications to graphs.  We will do a study of harmonic analysis on SL(2,Z)\SL(2,R), including the trace formula.  Other possible topics include

• Connections between Random Matrix Theory and the Riemann Hypothesis
• L-functions
• Irrationality of special values, such as zeta(3)
• Ramanujan and Selberg Conjectures
• Converse Theorem

 Stephen Miller, Dec 7, 2000.