### 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 language | English |
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Pages (from-to) | 317-369 |

Number of pages | 53 |

Journal | Israel Journal of Mathematics |

Volume | 187 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2012 Jan 1 |

Externally published | Yes |

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### 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.

Research output: Contribution to journal › Article

*Israel Journal of Mathematics*, vol. 187, no. 1, pp. 317-369. https://doi.org/10.1007/s11856-011-0084-7

}

TY - JOUR

T1 - Fourier expansion of Arakawa lifting I

T2 - An explicit formula and examples of non-vanishing lifts

AU - Murase, Atsushi

AU - Narita, Hiroaki

PY - 2012/1/1

Y1 - 2012/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=79955888481&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955888481&partnerID=8YFLogxK

U2 - 10.1007/s11856-011-0084-7

DO - 10.1007/s11856-011-0084-7

M3 - Article

AN - SCOPUS:79955888481

VL - 187

SP - 317

EP - 369

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

SN - 0021-2172

IS - 1

ER -