## Hiraku Atobe

Assistant Professor

### Approach Number Theory from the theory of Automorphic Representations

Department of Mathematics, Mathematics

Theme | Liftings of automorphic forms and classification of automorphic representations |

Field | The theory of automoprhic represetations |

Keyword | Automorhic represetations, Liftings of automorphic forms, Langlands correspondence |

#### Introduction of Research

Automorphic forms, which are functions with rich symmetry, give us several number theoritic infomation, such as analytic continuation and functional equations of L-functions.

I study automorphic representations, which are representations consists of automorphic forms.

Arthur's classification which is a classification of automorphic representations of classical groups, is difficult to understand.

My main research thema is to study Arthur's classification using liftings of automorphic forms.

#### Representative Achievements

Local theta correspondence of tempered representations and Langlands parameters.

Invent. Math. 210 (2017), no. 2, 341–415.

On the uniqueness of generic representations in an L-packet.

Int. Math. Res. Not. IMRN 2017, no. 23, 7051–7068.

The local theta correspondence and the local Gan-Gross-Prasad conjecture for the symplectic-metaplectic case.

Math. Ann. 371 (2018), no. 1-2, 225–295.

J. Number Theory 153 (2015) 158–229.

On the local Langlands correspondence and Arthur conjecture for even orthogonal groups.

Represent. Theory 21 (2017), 354–415.

Academic degree | Ph.D. |

Self Introduction | I am from Osaka. |

Affiliated academic society | The Mathematical Society of Japan |

Room address | Faculty of Science, Building No. 4 4-512 |