## Geometry and Analysis of Automorphic Forms of Several Variables: Proceedings of the International Symposium in Honor of Takayuki Oda on the Occasion of His 60th Birthday, Tokyo, Japan, 14-17 September 2009This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda''s 60th birthday. It presents both research and survey articles in the fields that are the main themes of his work. The volume may serve as a guide to developing areas as well as a resource for researchers who seek a broader view and for students who are beginning to explore automorphic form. |

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### Contents

The Birch and SwinnertonDyer conjecture for Qcurves and Odas period relations Henri Darmon Victor Rotger and Yu Zhao | 1 |

The supremum of Newton polygons of pdivisible groups with a given pkernel type Shushi Harashita | 41 |

Borcherds lifts on Sp2Z Bernhard Heim and Atsushi Murase | 56 |

The archimedean Whittaker functions on GL3 Miki Hirano Taku Ishii and Tadashi Miyazaki | 77 |

Arithmetic properties of padic elliptic logarithmic functions Noriko HirataKohno | 110 |

Spherical functions on U2nUn Un and hermitian Siegel series Yumiko Hironaka | 120 |

Fourier transforms of weighted orbital integrals on the real symplectic group of rank two Werner Hoffmann | 160 |

An AtkinLehner type theorem on Siegel modular forms and primitive Fourier coecients T Ibukiyama and H Katsurada | 196 |

Cohomology of Siegel modular varieties of genus 2 and corresponding automorphic forms Takayuki Oda | 211 |

Reducibility and discrete series in the case of classical padic groups an approach based on examples Marko Tadic | 254 |

A survey on Voronoıs theorem
Takao Watanabe | 334 |

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### Common terms and phrases

algebraic automorphic forms Borcherds lift Cartan subgroup character coefficients cohomology groups conjecture cuspidal representation defined definition denote discrete series dual element elliptic curve finite follows functional equations group G Heegner point hermitian holomorphic implies induced representations irreducible cuspidal representation irreducible representation irreducible square integrable irreducible subquotient isomorphism Jacquet module Jordan blocks K1 ml Lemma Levi subgroup linear groups Math matrix multiplicity Newton polygon number field obtain p-adic p-adic elliptic p-adic groups p-divisible groups parabolically induced representations principal series representations Proof Proposition proved quotient reducibility representation of G resp satisfies Shimura Siegel modular forms space spherical functions square integrable square integrable representations standard parabolic subgroup subquotient subrepresentation symmetric symplectic Theorem To(N trivial type one function unitary Whittaker functions