| Document Type
|
:
|
BL
|
| Record Number
|
:
|
890630
|
| Main Entry
|
:
|
Weng, Lin,1964-
|
| Title & Author
|
:
|
Zeta functions of reductive groups and their zeros /\ Lin Weng, Kyushu University, Japan.
|
| Publication Statement
|
:
|
New Jersey :: World Scientific,, [2018]
|
| Page. NO
|
:
|
1 online resource
|
| ISBN
|
:
|
9789813230651
|
|
|
:
|
: 9813230657
|
|
|
:
|
9789813231528
|
|
|
:
|
9813231521
|
| Bibliographies/Indexes
|
:
|
Includes bibliographical references and index.
|
| Contents
|
:
|
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
|
|
|
:
|
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
|
|
|
:
|
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
|
|
|
:
|
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
|
|
|
:
|
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
|
| Subject
|
:
|
Functions, Zeta.
|
| Subject
|
:
|
Linear algebraic groups.
|
| Subject
|
:
|
Functions, Zeta.
|
| Subject
|
:
|
Linear algebraic groups.
|
| Subject
|
:
|
MATHEMATICS-- Calculus.
|
| Subject
|
:
|
MATHEMATICS-- Mathematical Analysis.
|
| Dewey Classification
|
:
|
515/.56
|
| LC Classification
|
:
|
QA351.W46 2018
|