Fourier expansion of Arakawa lifting II: Relation with central L-values

Atsushi Murase, Hiroaki Narita

研究成果: Article

2 引用 (Scopus)

抜粋

This is a continuation of our previous paper [Fourier expansion of Arakawa lifting I: An explicit formula and examples of non-vanishing lifts, Israel J. Math. 187 (2012) 317-369]. The aim of the paper here is to study the Fourier coefficients of Arakawa lifts in relation with central values of automorphic L-functions. In the previous paper we provide an explicit formula for the Fourier coefficients in terms of toral integrals of automorphic forms on multiplicative groups of quaternion algebras. In this paper, after studying explicit relations between the toral integrals and the central L-values, we explicitly determine the constant of proportionality relating the square norm of a Fourier coefficient of an Arakawa lift with the central L-value. We can relate the square norm with the central value of some L-function of convolution type attached to the lift and a Hecke character. We also discuss the existence of strictly positive central values of the L-functions in our concern.

元の言語English
記事番号1650001
ジャーナルInternational Journal of Mathematics
27
発行部数1
DOI
出版物ステータスPublished - 2016 1 1
外部発表Yes

ASJC Scopus subject areas

  • Mathematics(all)

フィンガープリント Fourier expansion of Arakawa lifting II: Relation with central L-values' の研究トピックを掘り下げます。これらはともに一意のフィンガープリントを構成します。

  • これを引用