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)


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
Issue number1
Publication statusPublished - 2012 Jan 1


ASJC Scopus subject areas

  • Mathematics(all)

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