عنوان

Theta functions.

3642653154

9783642653155

b572079

Theta functions.

[Book]

Jun-Ichi Igusa

[Place of publication not identified]

Springer

2012

I. Theta Functions from an Analytic Viewpoint.- 1. Preliminaries.- 2. Plancherel Theorem for Rn.- 3. The Group A(X).- 4. The Irreducibility of U.- 5. Induced Representations.- 6. The Group Sp(X).- 7. The Group B(X).- 8. Fock Representation.- 9. The Set G(X).- 10. The Discrete Subgroup ?L.- II. Theta Functions from a Geometric Viewpoint.- 1. Hodge Decomposition Theorem for a Torus.- 2. Theta Function of a Positive Divisor.- 3. The Automorphy Factor u?(z).- 4. The Vector Space L(Q, l, ?).- 5. A Change of the Canonical Base.- III Graded Rings of Theta Functions.- 1. Graded Rings.- 2. Algebraic and Integral Dependence.- 3. Weierstrass Preparation Theorem.- 4. Geometric Lemmas.- 5. Automorphic Forms and Projective Embeddings.- 6. Polarized Abelian Varieties.- 7. Projective Embeddings.- 8. The Field of Abelian Functions.- IV. Equations Defining Abelian Varieties.- 1. Theta Relations (Classical Forms).- 2. A New Formalism.- 3. Theta Relations (Under the New Formalism).- 4. The Ideal of Relations.- 5. Quadratic Equations Defining Abelian Varieties.- V. Graded Rings of Theta Constants.- 1. Theta Constants.- 2. Some Properties of ?(?)2.- 3. Holomorphic Mappings by Theta Constants.- 4. The Classical Reduction Theory.- 5. Modular Forms.- 6. The Group of Characteristics.- 7. Modular Varieties.- Sources.- Further References and Comments.- Index of Definitions.

Jun-Ichi Igusa

Jun-Ichi Igusa

[Book]

Y