Mean Values of Derivatives of L-functions in Function Fields: II

Abstract

This is the second part of our investigation of mean values of derivatives of L-functions in function fields. In this paper, specifically, we prove several mean values results for the derivatives of L-functions in function fields when the average is taken over all discriminants, i.e., over all monic polynomials of a prescribed degree in Fq[T]. We establish exact formulas for the mean value of the m-th derivative of L-functions in function fields at the critical point and we compute a few particular examples.