### Abstract

We discuss a theta lifting from SL_{2} to O(3, 2), which will produce a certain class of residual cohomological automorphic forms on the orthogonal group. We will show an explicit formula for their Fourier expansions, in which the constant terms may also occur, by using the Fourier coefficients of a half-integral weight cusp form, which is similar to the classical formula for the holomorphic Saito-Kurokawa lifting at finite places.

Original language | English |
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Pages (from-to) | 139-163 |

Number of pages | 25 |

Journal | Manuscripta Mathematica |

Volume | 114 |

Issue number | 2 |

Publication status | Published - 2004 Jun |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Manuscripta Mathematica*,

*114*(2), 139-163.

**On Saito-Kurokawa lifting to cohomological Siegel modular forms.** / Miyazaki, Takuya.

Research output: Contribution to journal › Article

*Manuscripta Mathematica*, vol. 114, no. 2, pp. 139-163.

}

TY - JOUR

T1 - On Saito-Kurokawa lifting to cohomological Siegel modular forms

AU - Miyazaki, Takuya

PY - 2004/6

Y1 - 2004/6

N2 - We discuss a theta lifting from SL2 to O(3, 2), which will produce a certain class of residual cohomological automorphic forms on the orthogonal group. We will show an explicit formula for their Fourier expansions, in which the constant terms may also occur, by using the Fourier coefficients of a half-integral weight cusp form, which is similar to the classical formula for the holomorphic Saito-Kurokawa lifting at finite places.

AB - We discuss a theta lifting from SL2 to O(3, 2), which will produce a certain class of residual cohomological automorphic forms on the orthogonal group. We will show an explicit formula for their Fourier expansions, in which the constant terms may also occur, by using the Fourier coefficients of a half-integral weight cusp form, which is similar to the classical formula for the holomorphic Saito-Kurokawa lifting at finite places.

UR - http://www.scopus.com/inward/record.url?scp=3042813998&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3042813998&partnerID=8YFLogxK

M3 - Article

VL - 114

SP - 139

EP - 163

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

SN - 0025-2611

IS - 2

ER -