THE RECIPROCITY LAW FOR THE TWISTED SECOND MOMENT OF DIRICHLET L-FUNCTIONS OVER RATIONAL FUNCTION FIELDS

摘要

We prove the reciprocity law for the twisted second moments of Dirichlet L-functions over rational function fields, corresponding to two irreducible polynomials. This formula is the analogue of the formulas for Dirichlet L-functions over Q obtained by Conrey ['The mean-square of Dirichlet L-functions', arXiv:0708.2699 [math.NT] (2007)] and Young ['The reciprocity law for the twisted second moment of Dirichlet L-functions', Forum Math. 23(6) (2011), 1323-1337].