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

Atsushi Murase, Hiroaki Narita

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)317-369
Number of pages53
JournalIsrael Journal of Mathematics
Volume187
Issue number1
DOIs
Publication statusPublished - 2012 Jan 1
Externally publishedYes

Fingerprint

Automorphic Forms
Fourier Expansion
Explicit Formula
Quaternion Algebra
Imaginary Quadratic Field
Cusp Form
Unitary group
Fourier coefficients
Quaternion
Series
Character

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Fourier expansion of Arakawa lifting I : An explicit formula and examples of non-vanishing lifts. / Murase, Atsushi; Narita, Hiroaki.

In: Israel Journal of Mathematics, Vol. 187, No. 1, 01.01.2012, p. 317-369.

Research output: Contribution to journalArticle

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