The reciprocity law for the twisted second moment of Dirichlet L-functions

Abstract

We produce a new proof of the reciprocity law for the twisted second moment of Dirichlet L-functions that was recently proved by Conrey. Our method is to analyze certain two-variable sums where the variables satisfy a linear congruence. We show that these sums satisfy an elegant reciprocity formula. In the case that the modulus is prime, these sums are closely related to the twisted second moment, and the reciprocity formula for these sums implies Conrey's reciprocity formula. We also extend the range of uniformity of Conrey's formula.

arXiv comment12 pages

References in corpus (2)

• The mean-square of Dirichlet L-functions
• The fourth moment of Dirichlet $L$-functions

Cited by in corpus (9)

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• A note on additive twists, reciprocity laws and quantum modular forms
• Spectral Moment Formulae for $GL(3)\times GL(2)$ $L$-functions III: The Twisted Case
• Mixed moment of $GL(2)$ and $GL(3)$ $L$-functions
• Periods and Reciprocity II
• A congruence sum and rational approximations