Fourier expansion of Arakawa lifting I: An explicit formula and examples of non-vanishing lifts

Atsushi Murase, Hiroaki Narita

研究成果: Article査読

6 被引用数 (Scopus)

抄録

Given an elliptic cusp form f and an automorphic form f′ on a definite quaternion algebra over ℚ, there is a theta lifting from (f, f′) to an automorphic form L(f, f′) on the quaternion unitary group GSp(1, 1) generating quaternionic discrete series at the Archimedean place. The aim of this paper is to provide an explicit formula for Fourier coefficients of L(f, f′) in terms of periods of f and f′ with respect to a unitary character χ of an imaginary quadratic field. As an application, we show the existence of (f, f′) with L(f, f′) ≠ 0.

本文言語English
ページ(範囲)317-369
ページ数53
ジャーナルIsrael Journal of Mathematics
187
1
DOI
出版ステータスPublished - 2012 1 1
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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