School of Mathematics

Tony Scholl

Tony Scholl abstract

L-functions and arithmetic.

Many of the deepest problems in number theory are related to zeta- and L-functions. Most well-known is the connection between prime numbers and the Riemann zeta function (and more generally Dirichlet L-functions). L-functions are central to the conjectural Langlands correspondence relating automorphic forms and representations of Galois groups. The analytic behaviour of L-functions also is related in a subtle way to invariants of number fields, elliptic curves and other arithmetic and geometric objects. I shall give an overview of some of the ideas, results and open problems in this area.