#### Vol. 12, No. 3, 2019

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editors’ Interests Scientific Advantages Submission Guidelines Submission Form Ethics Statement Editorial Login Author Index Coming Soon Contacts ISSN: 1944-4184 (e-only) ISSN: 1944-4176 (print) Other MSP Journals
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
Primary: 11M20
##### Milestones
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