DATE:     Thursday, February 24, 2005
TIME:     12:10 pm in Weber 117
SPEAKER:  Andreas Stein, Department of Mathematics, Univ. of Wyoming
TITLE:    An Algorithm for Computing the Class Number of an Algebraic
          Function Field

ABSRTACT: A fundamental problem in the theory of function fields and curves
over finite fields is the effective computation of the class number h
and thus the order of the Jacobian of an algebraic function field. This
problem has important applications to cryptography since the Jacobians of
algebraic curves have been suggested to build cryptosystems. Popular
examples are ECC and HCC. If the characteristic of the finite field is
small, various recent algorithms solve this problem. Our main focus will
be algebraic function fields of large characteristic,  in which case not
much is known about effective computation of the order of the Jacobian. 

In our talk, we provide tight estimates for the  class number via
truncated Euler products, and show how these estimates can be used to
develop an effective method of computing h.