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Special Functions, KZ Type Equations, and Representation Theory

2003 Mathematics
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Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 673/5 ( reviews)

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Book Synopsis Special Functions, KZ Type Equations, and Representation Theory by : Aleksandr Nikolaevich Varchenko

Download or read book Special Functions, KZ Type Equations, and Representation Theory written by Aleksandr Nikolaevich Varchenko. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: The last twenty years have seen an active interaction between mathematics and physics. This book is devoted to one of the new areas which deals with mathematical structures related to conformal field theory and its sqs-deformations. In the book, the author discusses the interplay between Knizhnik-Zamolodchikov type equations, the Bethe ansatz method, representation theory, and geometry of multi-dimensional hypergeometric functions. This book aims to provide an introduction to the area and expose different facets of the subject. It contains constructions, discussions of notions, statements of main results, and illustrative examples. The exposition is restricted to the simplest case of the theory associated with the Lie algebra s\mathfrak{sl 2s. This book is intended for researchers and graduate students in mathematics and in mathematical physics, in particular to those interested in applications of special functions.

Special Functions and Orthogonal Polynomials

2016-05-17 Mathematics
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Release : 2016-05-17
Genre : Mathematics
Kind : eBook
Book Rating : 054/5 ( reviews)

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Book Synopsis Special Functions and Orthogonal Polynomials by : Richard Beals

Download or read book Special Functions and Orthogonal Polynomials written by Richard Beals. This book was released on 2016-05-17. Available in PDF, EPUB and Kindle. Book excerpt: The subject of special functions is often presented as a collection of disparate results, rarely organized in a coherent way. This book emphasizes general principles that unify and demarcate the subjects of study. The authors' main goals are to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more. It shows how much of the subject can be traced back to two equations - the hypergeometric equation and confluent hypergeometric equation - and it details the ways in which these equations are canonical and special. There is extended coverage of orthogonal polynomials, including connections to approximation theory, continued fractions, and the moment problem, as well as an introduction to new asymptotic methods. There are also chapters on Meijer G-functions and elliptic functions. The final chapter introduces Painlevé transcendents, which have been termed the 'special functions of the twenty-first century'.

Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions

2020-10-15 Mathematics
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Release : 2020-10-15
Genre : Mathematics
Kind : eBook
Book Rating : 554/5 ( reviews)

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Book Synopsis Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions by : Tom H. Koornwinder

Download or read book Encyclopedia of Special Functions: The Askey-Bateman Project: Volume 2, Multivariable Special Functions written by Tom H. Koornwinder. This book was released on 2020-10-15. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of three volumes that form the Encyclopedia of Special Functions, an extensive update of the Bateman Manuscript Project. Volume 2 covers multivariable special functions. When the Bateman project appeared, study of these was in an early stage, but revolutionary developments began to be made in the 1980s and have continued ever since. World-renowned experts survey these over the course of 12 chapters, each containing an extensive bibliography. The reader encounters different perspectives on a wide range of topics, from Dunkl theory, to Macdonald theory, to the various deep generalizations of classical hypergeometric functions to the several variables case, including the elliptic level. Particular attention is paid to the close relation of the subject with Lie theory, geometry, mathematical physics and combinatorics.

Bridging Algebra, Geometry, and Topology

2014-10-20 Mathematics
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Release : 2014-10-20
Genre : Mathematics
Kind : eBook
Book Rating : 867/5 ( reviews)

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Book Synopsis Bridging Algebra, Geometry, and Topology by : Denis Ibadula

Download or read book Bridging Algebra, Geometry, and Topology written by Denis Ibadula. This book was released on 2014-10-20. Available in PDF, EPUB and Kindle. Book excerpt: Algebra, geometry and topology cover a variety of different, but intimately related research fields in modern mathematics. This book focuses on specific aspects of this interaction. The present volume contains refereed papers which were presented at the International Conference “Experimental and Theoretical Methods in Algebra, Geometry and Topology”, held in Eforie Nord (near Constanta), Romania, during 20-25 June 2013. The conference was devoted to the 60th anniversary of the distinguished Romanian mathematicians Alexandru Dimca and Ştefan Papadima. The selected papers consist of original research work and a survey paper. They are intended for a large audience, including researchers and graduate students interested in algebraic geometry, combinatorics, topology, hyperplane arrangements and commutative algebra. The papers are written by well-known experts from different fields of mathematics, affiliated to universities from all over the word, they cover a broad range of topics and explore the research frontiers of a wide variety of contemporary problems of modern mathematics.

Zeta and $L$-functions in Number Theory and Combinatorics

2019-03-01 Mathematics
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Release : 2019-03-01
Genre : Mathematics
Kind : eBook
Book Rating : 005/5 ( reviews)

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Book Synopsis Zeta and $L$-functions in Number Theory and Combinatorics by : Wen-Ching Winnie Li

Download or read book Zeta and $L$-functions in Number Theory and Combinatorics written by Wen-Ching Winnie Li. This book was released on 2019-03-01. Available in PDF, EPUB and Kindle. Book excerpt: Zeta and L-functions play a central role in number theory. They provide important information of arithmetic nature. This book, which grew out of the author's teaching over several years, explores the interaction between number theory and combinatorics using zeta and L-functions as a central theme. It provides a systematic and comprehensive account of these functions in a combinatorial setting and establishes, among other things, the combinatorial counterparts of celebrated results in number theory, such as the prime number theorem and the Chebotarev density theorem. The spectral theory for finite graphs and higher dimensional complexes is studied. Of special interest in theory and applications are the spectrally extremal objects, called Ramanujan graphs and Ramanujan complexes, which can be characterized by their associated zeta functions satisfying the Riemann Hypothesis. Explicit constructions of these extremal combinatorial objects, using number-theoretic and combinatorial means, are presented. Research on zeta and L-functions for complexes other than graphs emerged only in recent years. This is the first book for graduate students and researchers offering deep insight into this fascinating and fast developing area.

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