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Bull. Korean Math. Soc. 2012; 49(5): 1007-1014

Printed September 30, 2012

https://doi.org/10.4134/BKMS.2012.49.5.1007

Copyright © The Korean Mathematical Society.

On some exact reciprocity formulas for twisted second moments of Dirichlet $L$-functions

Goran Djankovi{\' c}

University of Belgrade

Abstract

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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

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