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

The reciprocity law for the twisted second moment of Dirichlet L -functions 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

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

Forum Mathematicum , Volume 23 (6) – Nov 1, 2011

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Publisher
de Gruyter
Copyright
© de Gruyter 2011
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/FORM.2011.053
Publisher site
See Article on Publisher Site

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.

Journal

Forum Mathematicumde Gruyter

Published: Nov 1, 2011

Keywords: Moments; twisted reciprocity; Dirichlet L -function

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