Abstract :
Let F be a finite field with q elements, A = F[T] the polynomial ring over F, and K = F(T). If m A is a square-free polynomial, we denote by m the integral closure of A in k([formula]). In this paper we determine, roughly speaking, the average value of the size of the groups K2( m) as m varies of all square-free polynomials of a fixed degree M. The answer is a certain constant times q3(M/2) plus an error term of order qM. The constant is determined precisely.
