Mean Values of Derivatives of L-functions in Function Fields: III
Bueno De Andrade, J
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Cambridge University Press (CUP) for Royal Society of Edinburgh
Reason for embargo
This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by CUP
In this series of papers, we explore moments of derivatives of L-functions in function fields using classical analytic techniques such as character sums and approximate functional equation. The present paper is concerned with the study of mean values of derivatives of quadratic Dirichlet L-functions over function fields when the average is taken over monic and irreducible polynomials P in Fq[T]. When the cardinality q of the ground field is fixed and the degree of P gets large we obtain asymptotic formulas for the first moment of the first and the second derivative of this family of L-functions at the critical point. We also compute the full polynomial expansion in the asymptotic formulas for both mean values.