__This Course is Independent
of Last Semesters Course__

: 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 includeSummary

- 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.