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Record Nr. |
UNINA9910789812403321 |
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Autore |
Brubaker Ben <1976-> |
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Titolo |
Weyl group multiple Dirichlet [[electronic resource] /] / Ben Brubaker, Daniel Bump, and Solomon Friedberg |
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Pubbl/distr/stampa |
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Princeton, N.J., : Princeton University Press, c2011 |
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ISBN |
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1-283-01338-X |
9786613013385 |
1-4008-3899-1 |
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Edizione |
[Course Book] |
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Descrizione fisica |
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1 online resource (173 p.) |
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Collana |
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Annals of mathematics studies ; ; no. 175 |
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Altri autori (Persone) |
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BumpDaniel <1952-> |
FriedbergSolomon <1958-> |
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Disciplina |
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Soggetti |
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Dirichlet series |
Weyl groups |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Front matter -- Contents -- Preface -- Chapter One. Type A Weyl Group Multiple Dirichlet Series -- Chapter Two. Crystals and Gelfand-Tsetlin Patterns -- Chapter Three. Duality -- Chapter Four. Whittaker Functions -- Chapter Five. Tokuyama's Theorem -- Chapter Six. Outline of the Proof -- Chapter Seven. Statement B Implies Statement A -- Chapter Eight. Cartoons -- Chapter Nine. Snakes -- Chapter Ten. Noncritical Resonances -- Chapter Eleven. Types -- Chapter Twelve. Knowability -- Chapter Thirteen. The Reduction to Statement D -- Chapter Fourteen. Statement E Implies Statement D -- Chapter Fifteen. Evaluation of ΛΓ and ΛΔ, and Statement G -- Chapter Sixteen. Concurrence -- Chapter Seventeen. Conclusion of the Proof -- Chapter Eighteen. Statement B and Crystal Graphs -- Chapter Nineteen. Statement B and the Yang-Baxter Equation -- Chapter Twenty. Crystals and p-adic Integration -- Bibliography -- Notation -- Index |
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Sommario/riassunto |
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Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their |
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groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics. These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished. The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation. |
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2. |
Record Nr. |
UNINA9910821525603321 |
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Titolo |
Mechanical components and control engineering III : selected, peer reviewed papers from the 3rd Asian Pacific Conference on Mechanical Compenents and Control Engineering (ICMCCE 2014), September 20-21, 2014, Tianjin, China / / edited by Weimin Ge |
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Pubbl/distr/stampa |
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Pfaffikon, Switzerland : , : Trans Tech Publications Ltd, , 2014 |
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©2014 |
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ISBN |
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Descrizione fisica |
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1 online resource (1722 p.) |
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Collana |
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Applied Mechanics and Materials, , 1662-7482 ; ; Volume 668-669 |
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Disciplina |
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Soggetti |
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Machine parts |
Machine design |
Control systems |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references at the end of each chapters and indexes. |
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Nota di contenuto |
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Mechanical Components and Control Engineering III; Preface, Committees and Sponsor; Table of Contents; Chapter 1: Materials Science and Processing Technologies; Comparison Research of Aircraft Panels Connected by Friction Stir Welding and Riveting; Controllable Tuning of the Spin-Dependent Transport in the Graphene Sheet; Discrete Element Simulation and Analysis for Max Density Curve Theory of Mineral Aggregate Mixtures; Dispersion Management and Nonlinearity Enhancement in a Hybrid Nanofiber with a High Index, Cross-Slot-Structure Nanocore |
Effect of Carbon Nanotubes on Morphology and Property of Natural RubberFirst-Principles Study on Optical Properties of Cd-Doped Single-Walled (8, 0) ZnO Nanotube; Liquid Crystalline PET/60HBA-MWNTs Composite: Synthesis, Characterization, and Properties; Low Temperature Densification of ZnO-Based Ceramic Using Phenolic Resin as Binder; Mechanical Property and Corrosion Resistance of the E309L Buffer Layer in Weld Overlay; Multi Fractal Characteristic of Metal Material Worn Surface with Plant Abrasive |
Preparation and Photoluminescence of Red, Green and Blue Fluorescent Dyes Co-Doped Nanoporous Silica by a Sol-Gel MethodResearch on Distribution Regularity of Nano-Sized WC in Cast Steel; Research on Electrical Discharge Grinding of Polycrystalline Cubic Boron Nitride Cutting Tool; Simulation of Fiber Orientation in Dumbbell-Shaped Injection Cavity; Structural Phase Stability and Electronic Properties of Magnesium under High Pressure from First-Principles Calculations; Study of the Mechanical Properties of Ceramics Modified Composite Insulator Materials |
Study on the Critical Control of Foam Insulation Materials Produced by Waste TFT-LCD GlassSynthesis of a Cholesterylated Compound Containing Carboxyl Functional with PEG2000 Chain for Hepatic Targeting Liposome Ligand; The Analysis for Crystallization of Sn-Pb Alloys Using Acoustic Emission Testing about Wind Turbine Root Materials; The Original Carbon-Copper Compound as a New Source of Electric Power; Thermal Reaction Kinetics of Fly Ash Cement Paste at the Age of 28 Days; Ellipsometry Analysis of MgxZn1-xO Films on Silicon Substrates |
Failure Analysis of Differential Pressure Transmitter Impulse Pipe in High Sulfur Purification DeviceThe Research of the Structure and Performance Based on Quantum Dot Light Emitting Devices; Chapter 2: General Mechanical Engineering, Applied Mechanics and Dynamics; A New Approach for Determining Bolt Load of Eccentric Bolted Joints; A New Numerical Method for Two Phase Flow in Heterogeneous Porous Media; A Novel Tyre Force Distribution Method for Four-Wheel Independent Driving Vehicles; A Prediction Model for Equivalent Parameters of Cylindrical Fixed Joint |
A Study on Conjugate Cam Beating-Up Mechanism |
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Sommario/riassunto |
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Collection of selected, peer reviewed papers from the 3 rd Asian Pacific Conference on Mechanical Components and Control Engineering (MCCE 2014), September 20-21, 2014, Tianjin, China. The 367 papers are grouped as follows: Chapter 1: Materials Science and Processing Technologies, Chapter 2: General Mechanical Engineering, Applied Mechanics and Dynamics, Chapter 3: Mechatronics and Robotics, Chapter 4: Control Technologies, Automation, Design and Simulation of Manufacturing, Chapter 5: Electrical Engineering and Electric Machines, Chapter 6: Power System and Energy Engineering, its Application |
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