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

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. 2011 de Gruyter.

authors

• Young, Matthew

published proceedings

• FORUM MATHEMATICUM

author list (cited authors)

• Young, M. P.

citation count

• 11

complete list of authors

• Young, Matthew P

publication date

• November 2011

publisher

• DE GRUYTER  Publisher

published in

• Forum Mathematicum  Journal

keywords

• Dirichlet L-function
• Moments
• Twisted Reciprocity

Digital Object Identifier (DOI)

• 10.1515/FORM.2011.053

start page

• 1323

end page

• 1337

volume

• 23

issue

• 6

URL

• http%3A%2F%2Fdx.doi.org%2F10.1515%2Fform.2011.053