Vol. 12, No. 3, 2019

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Effective moments of Dirichlet $L$-functions in Galois orbits

Rizwanur Khan, Ruoyun Lei and Djordje Milićević

Vol. 12 (2019), No. 3, 475–490
Abstract

Khan, Milićević, and Ngo evaluated the second moment of L-functions associated to certain Galois orbits of primitive Dirichlet characters to modulus a large power of any fixed odd prime p. Their results depend on p-adic Diophantine approximation and are ineffective, in the sense of computability. We obtain an effective asymptotic for this second moment in the case of p = 3,5,7.

Keywords
$L$-functions, Dirichlet characters, moments
Mathematical Subject Classification 2010
Primary: 11M20
Milestones
Received: 29 December 2017
Revised: 19 September 2018
Accepted: 12 October 2018
Published: 14 December 2018

Communicated by Stephan Garcia
Authors
Rizwanur Khan
Department of Mathematics
University of Mississippi
University, MS
United States
Ruoyun Lei
Department of Mathematics
Bryn Mawr College
Bryn Mawr, PA
United States
Djordje Milićević
Department of Mathematics
Bryn Mawr College
Bryn Mawr, PA
United States