Vector-valued p-adic Siegel modular forms
Abstract.
We study vector-valued p-adic Siegel modular forms based on the arithmetic theory of vector-valued Siegel modular forms over rings. We construct Fourier expansions and Hecke operators for these modular forms, and especially, using the description of these p-adic forms on the Igusa tower, we give a natural definition of p-adic operators.
This paper is written based on my seminar talk at Muroran in March 2010. I deeply thank the organizer Professor Hidenori Katsurada, and also thank Professor Iku Nakamura and Dr. Hisa-aki Kawamura who pointed out my mistakes and gave valuable remarks at this seminar. Furthermore, I sincerely thank the referee, who read the first version carefully and gave useful comments.
© 2014 by Walter de Gruyter Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- UC hierarchy and monodromy preserving deformation
- Vector-valued p-adic Siegel modular forms
- K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux
-
Strichartz estimates for partially periodic solutions to Schrödinger equations in
- Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
- Mean curvature flow of entire graphs in a half-space with a free boundary
- Ricci flow and the holonomy group
- Uniqueness of compact tangent flows in Mean Curvature Flow
- Even unimodular Lorentzian lattices and hyperbolic volume
- Algebraic points on Shimura curves of Γ0(p)-type
- Errata to Algebraic points on Shimura curves of Γ0(p)-type (J. reine angew. Math., DOI 10.1515/crelle-2012-0068)
- Property A and the operator norm localization property for discrete metric spaces
- Stable manifolds for holomorphic automorphisms
Artikel in diesem Heft
- Frontmatter
- UC hierarchy and monodromy preserving deformation
- Vector-valued p-adic Siegel modular forms
- K-theoretic Schubert calculus for OG(n,2n+1) and jeu de taquin for shifted increasing tableaux
-
Strichartz estimates for partially periodic solutions to Schrödinger equations in
- Inverse tunneling estimates and applications to the study of spectral statistics of random operators on the real line
- Mean curvature flow of entire graphs in a half-space with a free boundary
- Ricci flow and the holonomy group
- Uniqueness of compact tangent flows in Mean Curvature Flow
- Even unimodular Lorentzian lattices and hyperbolic volume
- Algebraic points on Shimura curves of Γ0(p)-type
- Errata to Algebraic points on Shimura curves of Γ0(p)-type (J. reine angew. Math., DOI 10.1515/crelle-2012-0068)
- Property A and the operator norm localization property for discrete metric spaces
- Stable manifolds for holomorphic automorphisms
