Lecture 1. Tuesday, May 3, 4:00 p.m., 314 Altgeld Hal1
Families of zeta functions and symmetry
- A reception will be held Tuesday, May 3, from 5:00-6:00
p.m., in 314A Illini Union
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Lecture 2. Wednesday, May 4, 4:00 p.m., 245 Altgeld
Hall
Ramanujan's conjecture and its generalizations
Lecture 3. Thursday, May 5, 11:00 a.m., 245 Altgeld Hall
Ramanujan's conjecture and its generalizations
Zeta (and L) functions are associated with automorphic
forms. One of the main themes in the study of the zeroes of these
functions, is that of a family. We describe some recent developments,
applications and conjectures in the theory. In particular we highlight
the role played by symmetry types (from random matrix theory) that
are associated with a family. This will then be applied to the generalized
Ramanujan conjectures, which we will introduce and discuss in some
detail.
