Mean value theorems for L-functions over prime polynomials for the rational function field

Julio C. Andrade, and Jonathan P. Keating. "Mean value theorems for L-functions over prime polynomials for the rational function field." Acta Arithmetica 161.4 (2013): 371-385. <http://eudml.org/doc/279580>.

@article{JulioC2013,
abstract = {The first and second moments are established for the family of quadratic Dirichlet L-functions over the rational function field at the central point s=1/2, where the character χ is defined by the Legendre symbol for polynomials over finite fields and runs over all monic irreducible polynomials P of a given odd degree. Asymptotic formulae are derived for fixed finite fields when the degree of P is large. The first moment obtained here is the function field analogue of a result due to Jutila in the number field setting. The approach is based on classical analytical methods and relies on the use of the analogue of the approximate functional equation for these L-functions.},
author = {Julio C. Andrade, Jonathan P. Keating},
journal = {Acta Arithmetica},
keywords = {finite fields; function field; hyperelliptic curve; moments of quadratic Dirichlet L-function; prime polynomial},
language = {eng},
number = {4},
pages = {371-385},
title = {Mean value theorems for L-functions over prime polynomials for the rational function field},
url = {http://eudml.org/doc/279580},
volume = {161},
year = {2013},
}

TY - JOUR
AU - Julio C. Andrade
AU - Jonathan P. Keating
TI - Mean value theorems for L-functions over prime polynomials for the rational function field
JO - Acta Arithmetica
PY - 2013
VL - 161
IS - 4
SP - 371
EP - 385
AB - The first and second moments are established for the family of quadratic Dirichlet L-functions over the rational function field at the central point s=1/2, where the character χ is defined by the Legendre symbol for polynomials over finite fields and runs over all monic irreducible polynomials P of a given odd degree. Asymptotic formulae are derived for fixed finite fields when the degree of P is large. The first moment obtained here is the function field analogue of a result due to Jutila in the number field setting. The approach is based on classical analytical methods and relies on the use of the analogue of the approximate functional equation for these L-functions.
LA - eng
KW - finite fields; function field; hyperelliptic curve; moments of quadratic Dirichlet L-function; prime polynomial
UR - http://eudml.org/doc/279580
ER -