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Field name	Details
Dewey Class	515
Title	Theta Functions ([EBook]) / by Jun-ichi Igusa.
Author	Igusa, Jun-ichi. , 1924-
Other name(s)	SpringerLink (Online service)
Publication	Berlin, Heidelberg : Springer , 1972.
Physical Details	X, 234 pages : online resource.
Series	Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 0072-7830 ; ; 194
ISBN	9783642653155
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-642-65315-5
Links to Related Works	Subject References: Analysis . Analysis (Mathematics) . Mathematical analysis . Mathematics . Authors: Igusa, Jun-ichi. 1924- . Igusa, Jun-ichi, 1924- . Corporate Authors: SpringerLink (Online service) . Series: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete . Classification: 515 .

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Theta Functions

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