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The reciprocity law for the twisted second moment of Dirichlet L-functions
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Matthew P. Young
Published/Copyright:
June 27, 2010
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.
Received: 2007-09-09
Revised: 2010-02-25
Published Online: 2010-06-27
Published in Print: 2011-November
© de Gruyter 2011
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Articles in the same Issue
- Almost global existence for quasilinear wave equations with inhomogeneous terms in 3D
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- Weighted energy estimates for wave equations in exterior domains
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