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 On some exact reciprocity formulas for twisted second moments of Dirichlet $L$-functions Bull. Korean Math. Soc. 2012 Vol. 49, No. 5, 1007-1014 https://doi.org/10.4134/BKMS.2012.49.5.1007Printed September 30, 2012 Goran Djankovi{\' c} University of Belgrade Abstract : We derive the exact reciprocity formula connecting the twisted second moments at 1 for families of odd Dirichlet characters corresponding to two prime moduli, which parallels such formula discovered earlier for the special point $1/2$. Keywords : Dirichlet $L$-functions, special values, twisted moments, Bernoulli polynomials, Dedekind sums MSC numbers : 11M06, 11B68, 11F20 Downloads: Full-text PDF