3:00 p.m., Friday (October 19, 2007)
Math Annex 1100
Special values of L-functions modulo p
It has been known since Euler that the values of the Riemann zeta function at
negative integers are certain rational numbers, namely the Bernoulli numbers
B_k. Similarly, the values of Dirichlet L-functions at s=0 are related to class
numbers of certain number fields. These are simple instances of a common phenomenon,
namely that the values of L-functions at critical points are algebraic, up to a
simple factor, and that these algebraic numbers are related to algebraic quantities
such as class numbers and Selmer groups. The present talk will be a survey talk
on the algebraicity of special values of L-functions and their divisibility
properties modulo primes.
Refreshments will be served at 2:45 p.m. (Math Lounge, MATX 1115).