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, 2009 / editors, Yoshinori Hamahata ... [et al.].

Format:

Book

Conference/Event

Author/Creator:

International Symposium "Geometry and Analysis of Automorphic Forms of Several Variables", Corporate Author.

Contributor:

Oda, Takayuki.

Hamahata, Yoshinori.

Conference Name:

Geometry and Analysis of Automorphic Forms of Several Variables (2009 : Tokyo, Japan)

International Symposium [on] Geometry and Analysis of Automorphic Forms of Several Variables (2009 : Tokyo, Japan)

Series:

Series on number theory and its application ; v. 7.

Series on number theory and its application, 1793-3161 ; v. 7

Language:

English

Subjects (All):

Geometry--Congresses.

Geometry.

Automorphic forms--Congresses.

Automorphic forms.

Physical Description:

1 online resource (388 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; Hackensack, N.J. : World Scientific, c2012.

Language Note:

English

Summary:

This 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.

Contents:

Preface; Program of symposium; Contents; The Birch and Swinnerton-Dyer conjecture for Q-curves and Oda's period relations Henri Darmon, Victor Rotger and Yu Zhao; 1. Introduction; 2. Background; 2.1. The Birch and Swinnerton-Dyer conjecture in low analytic rank; 2.2. Oda's period relations and ATR points; 3. The Birch and Swinnerton-Dyer conjecture for Q-curves; 3.1. Review of Q-curves; 3.2. The main result; 4. Heegner points on Shimura's elliptic curves; 4.1. An explicit Heegner point construction; 4.2. Heegner points and ATR cycles; 4.3. Numerical examples; 4.4. Proof of Proposition 4.1

ReferencesThe supremum of Newton polygons of p-divisible groups with a given p-kernel type Shushi Harashita; 1. Introduction; 2. A catalogue of p-divisible groups with a given type; 3. Preliminaries on F-zips; 4. Lifting of F-zips; 5. A reduction of the problem; 6. Extensions by a minimal p-divisible group; 7. Proof of Proposition 5.2; References; Borcherds lifts on Sp2(Z) Bernhard Heim and Atsushi Murase; 1. Introduction and the main results; 1.1. Introduction; 1.2. Siegel modular forms; 1.3. The organization of the paper; 1.4. Notation; 2. Borcherds lifts; 2.1. Jacobi forms

2.2. Humbert surfaces2.3. Siegel modular forms with a nontrivial character; 2.4. Borcherds lifts on; 2.5. Examples of Borcherds lifts; 3. Proof of the main results; 3.1. The multiplicative symmetry; 3.2. A characterization of powers of the modular discriminant; 3.3. The multiplicative symmetry for Sym2(Mk( 1)); 3.4. Proofs of Theorem 1.1 and Theorem 1.2 (i); 4. The weight formula; 4.1. Cohen numbers; 4.2. The weight formula for Borcherds lifts; Acknowledgement; References; The archimedean Whittaker functions on GL(3) Miki Hirano, Taku Ishii and Tadashi Miyazaki; 1. Introduction

2. Preliminaries2.1. Notation; 2.2. Basic objects; 2.3. Whittaker functions on Gn; 2.5. The contragradient Whittaker functions; 2.6. The generalized principal series representations of Gn = GL(n; R); 2.7. The principal series representations of Gn = GL(n; C); 3. Whittaker functions on G3 = GL(3; R); 3.1. Irreducible representations of K3 = O(3); 3.2. Whittaker functions on G3 = GL(3; R) at the minimal K3-types; 3.3. Whittaker functions on G3 = GL(3; R) at the multiplicity one K3-types; 4. Whittaker functions on G3 = GL(3; C); 4.1. Irreducible representations of K3 = U(3)

4.2. Whittaker functions on G3 = GL(3 C) at the minimal K3-types; 5. The archimedean local theory of the standard L-functions for GL(n1) GL(n2) (n1 > n2); 5.1. The local Langlands correspondence for GL(n) over R; 5.2. The local Langlands correspondence for GL(n) over C; 5.3. The archimedean zeta integrals for GL(n1) GL(n2) (n1 > n2); 6. Calculus of the archimedean zeta integrals; 6.1. The archimedean zeta integrals for GL(3) GL(1); 6.2. The proof of Theorem 6.1; 6.3. The archimedean zeta integrals for GL(3) GL(2); References

Arithmetic properties of p-adic elliptic logarithmic functions Noriko Hirata-Kohno

Notes:

"Proceedings of the International Symposium "Geometry and Analysis of Automorphic Forms of Several Variables" ... consists of selected papers by the principal speakers of the symposium"--Preface.

Includes bibliographical references.

ISBN:

9786613555410

9781280376030

1280376031

9789814355605

9814355607

OCLC:

877767504