عنوان
پدید آورنده
موضوع
رده
QA351 .W46 2018
QA351
.
W46
2018
کتابخانه
محل استقرار
INTERNATIONAL STANDARD BOOK NUMBER
(Number (ISBN
9789813230651
(Number (ISBN
9813230657
Erroneous ISBN
9789813231528
Erroneous ISBN
9813231521
TITLE AND STATEMENT OF RESPONSIBILITY
Title Proper
Zeta functions of reductive groups and their zeros /
General Material Designation
[Book]
First Statement of Responsibility
Lin Weng, Kyushu University, Japan.
.PUBLICATION, DISTRIBUTION, ETC
Place of Publication, Distribution, etc.
New Jersey :
Name of Publisher, Distributor, etc.
World Scientific,
Date of Publication, Distribution, etc.
[2018]
PHYSICAL DESCRIPTION
Specific Material Designation and Extent of Item
1 online resource
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
Text of Note
Includes bibliographical references and index.
CONTENTS NOTE
Text of Note
Intro; Contents; Introduction; Non-Abelian Zeta Functions; 1. Semi-Stable Lattice; 1.1 Motivation; 1.2 Projective Modules; 1.2.1 Invertible Modules; 1.2.2 General Projective Modules; 1.3 Stability of Lattices; 1.3.1 Lattices; 1.3.2 Covolumes of Lattices; 1.3.3 Stability of Lattices; 1.3.4 Canonical Filtration; 1.4 Volume of Lattice: Special Linear Group; 1.4.1 Metrics of Lattices; 1.4.2 Special Metrics of Lattices; 1.5 Automorphisms of Lattices; 1.5.1 General Automorphisms; 1.5.2 Special Automorphisms; 1.5.3 Unit Automorphisms; 1.6 Compact Moduli Spaces of Semi-Stable Lattices
Text of Note
2. Geometry of Numbers2.1 Global Cohomology; 2.1.1 Adelic Ring; 2.1.2 Adelic Cohomology Groups; 2.1.3 Topological Duality: Local and Global Pairings; 2.2 Duality and Riemann-Roch Theorem in Arithmetic; 2.2.1 Nine-Diagram; 2.2.2 Arithmetic Riemann-Roch Theorem; 2.3 Arithmetic Vanishing Theorem; 2.3.1 Elementary Properties of 0-th Cohomology; 2.3.2 Ampleness and Vanishing Theorem; 3. Non-Abelian Zeta Functions; 3.1 Moduli Spaces of Semi-Stable Lattices; 3.1.1 Stability; 3.1.2 Effective Vanishing Theorem; 3.2 Non-Abelian Zeta Function; 3.2.1 Definition; 3.2.2 Zeta Properties
Text of Note
3.2.3 Relation with Epstein Zeta Function3.2.4 Riemann Hypothesis; Rank Two Zeta Functions; 4. Distances to Cusps and Fundamental Domains; 4.1 Upper Half Space Model; 4.1.1 Upper Half Plane; 4.1.2 Upper Half Space; 4.1.3 Rank Two OK-Lattices: Upper Half Space Model; 4.2 Cusps and Ideal Classes; 4.2.1 Generators of Fractional Ideals; 4.2.2 Special Transformations; 4.2.3 Cusps and Ideal Classes for Total Real Fields; 4.2.4 Cusps and Ideal Classes; 4.3 Stabilizers of Cusps and Their Fundamental Domains; 4.3.1 Upper Half Plane; 4.3.2 Upper Half Space
Text of Note
4.3.3 Fundamental Domains for Stabilizer Groups (I)4.3.3.1 Hilbert Modular Group; 4.3.3.2 Stabilizer Groups of Cusps; 4.3.3.3 Fundamental Domain of Cusp Stabilizers; 4.3.4 Fundamental Domains for Stabilizer Groups (II); 4.3.4.1 Stabilizer Groups; 4.3.4.2 Fundamental Domain of Stabilizer Group; 4.4 Distance to Cusp and Fundamental Domain; 4.4.1 Upper Half Plane; 4.4.2 Upper Half Space; 4.4.3 Fundamental Domain (I); 4.4.3.1 Primitive Distance To Cusp; 4.4.3.2 Fundamental Domain in Case of Totally Real Field; 4.4.4 Fundamental Domain (II); 4.4.4.1 Distance to Cusps; 4.4.4.2 Fundamental Domain
Text of Note
5. Rank Two Zeta Functions5.1 Distance to Cusp and Stability; 5.1.1 Parameter Space of Semi-Stable Rank Two Lattices; 5.1.2 Rank One Sub-Lattices; 5.1.3 Stability and Distances to Cusps; 5.1.4 Example: Truncated Fundamental Domain; 5.1.5 Moduli Space of Rank Two Semi-Stable Lattices; 5.2 Rank Two Non-Abelian Zeta Function; 5.2.1 Definition; 5.2.2 Relations with Epstein Zeta Functions; 5.3 Epstein Zeta Function and Its Fourier Expansion; 5.3.1 Automorphic Function in One Variable; 5.3.2 Upper Half Space; 5.3.2.1 Eisenstein Series over 3-Dimensional Hyperbolic Space
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OTHER EDITION IN ANOTHER MEDIUM
Title
Zeta functions of reductive groups and their zeros.
International Standard Book Number
9789813231528
TOPICAL NAME USED AS SUBJECT
Functions, Zeta.
Linear algebraic groups.
Functions, Zeta.
Linear algebraic groups.
MATHEMATICS-- Calculus.
MATHEMATICS-- Mathematical Analysis.
(SUBJECT CATEGORY (Provisional
MAT-- 005000
MAT-- 034000
DEWEY DECIMAL CLASSIFICATION
Number
515/
.
56
Edition
23
LIBRARY OF CONGRESS CLASSIFICATION
Class number
QA351
Book number
.
W46
2018
PERSONAL NAME - PRIMARY RESPONSIBILITY
Weng, Lin,1964-
ORIGINATING SOURCE
Date of Transaction
20200823231922.0
Cataloguing Rules (Descriptive Conventions))
pn
ELECTRONIC LOCATION AND ACCESS
Electronic name
مطالعه متن کتاب [Book]
Y
