The fourth moment of quadratic Dirichlet L-functions over function fields

We obtain an asymptotic formula for the fourth moment of quadratic Dirichlet L -functions over F q [ x ] , as the base field F q is fixed and the genus of the family goes to infinity. According to conjectures of Andrade and Keating, we expect the fourth moment to be asymptotic to q 2 g + 1 P ( 2 g +...

Full description

Saved in:
Bibliographic Details
Published inGeometric and functional analysis Vol. 27; no. 3; pp. 541 - 595
Main Author Florea, Alexandra
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2017
Springer Nature B.V
Subjects
Analysis
Asymptotic methods
Asymptotic properties
Dirichlet problem
Functions (mathematics)
Infinity
Mathematical analysis
Mathematics
Mathematics and Statistics
Online AccessGet full text

Cover

More Information
Summary:We obtain an asymptotic formula for the fourth moment of quadratic Dirichlet L -functions over F q [ x ] , as the base field F q is fixed and the genus of the family goes to infinity. According to conjectures of Andrade and Keating, we expect the fourth moment to be asymptotic to q 2 g + 1 P ( 2 g + 1 ) up to an error of size o ( q 2 g + 1 ) , where P is a polynomial of degree 10 with explicit coefficients. We prove an asymptotic formula with the leading three terms, which agrees with the conjectured result.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-017-0409-8