From: Brenda Cook (brenda@math.missouri.edu)
Date: Fri Feb 09 2007 - 08:07:28 CST
COLLOQUIUM
University of Missouri-Columbia
Department of Mathematics
Matthew P. Young
American Institute of Mathematics
Moments of Dirichlet L-functions and average ranks of elliptic curves
Abstract: An L-function is a special type of holomorphic function that
encodes arithmetical information. For example, properties of the
Riemann zeta function can give information about the distribution of the
prime numbers. Similarly, Dirichlet L-functions are used to count
primes in arithmetic progressions, and elliptic curve L-functions are
conjectured to detect if cubic diophantine equations have infinitely
many rational solutions or not.
In this talk I will tell the story of how L-functions relate to
arithmetic, and describe some recent advances in our understanding of
L-functions. In particular, I will discuss some results on mean values
of Dirichlet L-functions, and on average ranks of elliptic curves.
3:30 p.m.
Monday, February 12
210 General Classroom Building
Refreshments will be served at 2:45 p.m. in Room 326 Mathematical
Sciences (Math Lounge).
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