Hypergeometric Functions My Love

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Hypergeometric Functions, My Love

Author : Masaaki Yoshida
Publisher : Springer Science & Business Media
ISBN 13 : 3322901661
Total Pages : 301 pages
Book Rating : 4.3/5 (229 download)

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Book Synopsis Hypergeometric Functions, My Love by : Masaaki Yoshida

Download or read book Hypergeometric Functions, My Love written by Masaaki Yoshida and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical story - of the hypergeometric functions, the configuration space of 4 points on the projective line, elliptic curves, elliptic modular functions and the theta functions - now evolves, in this book, to the story of hypergeometric funktions in 4 variables, the configuration space of 6 points in the projective plane, K3 surfaces, theta functions in 4 variables. This modern theory has been established by the author and his collaborators in the 1990's; further development to different aspects is expected. It leads the reader to a fascinating 4-dimensional world. The author tells the story casually and visually in a plain language, starting form elementary level such as equivalence relations, the exponential function, ... Undergraduate students should be able to enjoy the text.

Basic Hypergeometric Series

Author : George Gasper
Publisher :
ISBN 13 : 0511889186
Total Pages : 456 pages
Book Rating : 4.5/5 (118 download)

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Book Synopsis Basic Hypergeometric Series by : George Gasper

Download or read book Basic Hypergeometric Series written by George Gasper and published by . This book was released on 2011-02-25 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Significant revision of classic reference in special functions.

Theory of Hypergeometric Functions

Author : Kazuhiko Aomoto
Publisher : Springer Science & Business Media
ISBN 13 : 4431539387
Total Pages : 327 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Theory of Hypergeometric Functions by : Kazuhiko Aomoto

Download or read book Theory of Hypergeometric Functions written by Kazuhiko Aomoto and published by Springer Science & Business Media. This book was released on 2011-05-21 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a geometric theory of complex analytic integrals representing hypergeometric functions of several variables. Starting from an integrand which is a product of powers of polynomials, integrals are explained, in an open affine space, as a pair of twisted de Rham cohomology and its dual over the coefficients of local system. It is shown that hypergeometric integrals generally satisfy a holonomic system of linear differential equations with respect to the coefficients of polynomials and also satisfy a holonomic system of linear difference equations with respect to the exponents. These are deduced from Grothendieck-Deligne’s rational de Rham cohomology on the one hand, and by multidimensional extension of Birkhoff’s classical theory on analytic difference equations on the other.

Hypergeometric Functions Over Finite Fields

Author : Jenny Fuselier
Publisher : American Mathematical Society
ISBN 13 : 1470454335
Total Pages : 138 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hypergeometric Functions Over Finite Fields by : Jenny Fuselier

Download or read book Hypergeometric Functions Over Finite Fields written by Jenny Fuselier and published by American Mathematical Society. This book was released on 2022-11-10 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Arithmetic and Geometry Around Hypergeometric Functions

Author : Rolf-Peter Holzapfel
Publisher : Springer Science & Business Media
ISBN 13 : 3764382848
Total Pages : 441 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Arithmetic and Geometry Around Hypergeometric Functions by : Rolf-Peter Holzapfel

Download or read book Arithmetic and Geometry Around Hypergeometric Functions written by Rolf-Peter Holzapfel and published by Springer Science & Business Media. This book was released on 2007-06-28 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises lecture notes, survey and research articles originating from the CIMPA Summer School Arithmetic and Geometry around Hypergeometric Functions held at Galatasaray University, Istanbul, June 13-25, 2005. It covers a wide range of topics related to hypergeometric functions, thus giving a broad perspective of the state of the art in the field.

Hessian Polyhedra, Invariant Theory And Appell Hypergeometric Functions

Author : Lei Yang
Publisher : World Scientific
ISBN 13 : 9813209496
Total Pages : 317 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Hessian Polyhedra, Invariant Theory And Appell Hypergeometric Functions by : Lei Yang

Download or read book Hessian Polyhedra, Invariant Theory And Appell Hypergeometric Functions written by Lei Yang and published by World Scientific. This book was released on 2018-03-13 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our book gives the complex counterpart of Klein's classic book on the icosahedron. We show that the following four apparently disjoint theories: the symmetries of the Hessian polyhedra (geometry), the resolution of some system of algebraic equations (algebra), the system of partial differential equations of Appell hypergeometric functions (analysis) and the modular equation of Picard modular functions (arithmetic) are in fact dominated by the structure of a single object, the Hessian group $mathfrak{G}’_{216}$. It provides another beautiful example on the fundamental unity of mathematics.

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

Author : Tom H. Koornwinder
Publisher : Cambridge University Press
ISBN 13 : 1108916554
Total Pages : 442 pages
Book Rating : 4.1/5 (89 download)

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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 and published by Cambridge University Press. This book was released on 2020-10-15 with total page 442 pages. 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.

Multivariate Normal Distribution, The: Theory And Applications

Author : Thu Pham-gia
Publisher : World Scientific
ISBN 13 : 9811235309
Total Pages : 494 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Multivariate Normal Distribution, The: Theory And Applications by : Thu Pham-gia

Download or read book Multivariate Normal Distribution, The: Theory And Applications written by Thu Pham-gia and published by World Scientific. This book was released on 2021-05-05 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with user-friendly applications of normal distribution. In several variables it is called the multinormal distribution which is often handled using matrices for convenience. The author seeks to make the arguments less abstract and hence, starts with the univariate case and moves progressively toward the vector and matrix cases. The approach used in the book is a gradual one, going from one scalar variable to a vector variable and to a matrix variable. The author presents the unified aspect of normal distribution, as well as addresses several other issues, including random matrix theory in physics. Other well-known applications, such as Herrnstein and Murray's argument that human intelligence is substantially influenced by both inherited and environmental factors, will be discussed in this book. It is a better predictor of many personal dynamics — including financial income, job performance, birth out of wedlock, and involvement in crime — than are an individual's parental socioeconomic status, or education level, and deserve to be mentioned and discussed.

Gröbner Deformations of Hypergeometric Differential Equations

Author : Mutsumi Saito
Publisher : Springer Science & Business Media
ISBN 13 : 366204112X
Total Pages : 261 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Gröbner Deformations of Hypergeometric Differential Equations by : Mutsumi Saito

Download or read book Gröbner Deformations of Hypergeometric Differential Equations written by Mutsumi Saito and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of Gröbner bases is a main tool for dealing with rings of differential operators. This book reexamines the concept of Gröbner bases from the point of view of geometric deformations. The algorithmic methods introduced in this book are particularly useful for studying the systems of multidimensional hypergeometric PDE's introduced by Gelfand, Kapranov, and Zelevinsky. A number of original research results are contained in the book, and many open problems are raised for future research in this rapidly growing area of computational mathematics.

Algebra, Geometry and Software Systems

Author : Michael Joswig
Publisher : Springer Science & Business Media
ISBN 13 : 3662051486
Total Pages : 332 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Algebra, Geometry and Software Systems by : Michael Joswig

Download or read book Algebra, Geometry and Software Systems written by Michael Joswig and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of surveys and research papers on mathematical software and algorithms. The common thread is that the field of mathematical applications lies on the border between algebra and geometry. Topics include polyhedral geometry, elimination theory, algebraic surfaces, Gröbner bases, triangulations of point sets and the mutual relationship. This diversity is accompanied by the abundance of available software systems which often handle only special mathematical aspects. This is why the volume also focuses on solutions to the integration of mathematical software systems. This includes low-level and XML based high-level communication channels as well as general frameworks for modular systems.

Arrangements, Local Systems and Singularities

Author : Fouad El Zein
Publisher : Springer Science & Business Media
ISBN 13 : 303460209X
Total Pages : 325 pages
Book Rating : 4.0/5 (346 download)

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Book Synopsis Arrangements, Local Systems and Singularities by : Fouad El Zein

Download or read book Arrangements, Local Systems and Singularities written by Fouad El Zein and published by Springer Science & Business Media. This book was released on 2010-03-14 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the Lecture Notes of the CIMPA/TUBITAK Summer School Arrangements, Local systems and Singularities held at Galatasaray University, Istanbul during June 2007. The volume is intended for a large audience in pure mathematics, including researchers and graduate students working in algebraic geometry, singularity theory, topology and related fields. The reader will find a variety of open problems involving arrangements, local systems and singularities proposed by the lecturers at the end of the school.

Symmetries, Integrable Systems and Representations

Author : Kenji Iohara
Publisher : Springer Science & Business Media
ISBN 13 : 1447148630
Total Pages : 633 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Symmetries, Integrable Systems and Representations by : Kenji Iohara

Download or read book Symmetries, Integrable Systems and Representations written by Kenji Iohara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Feynman Integrals

Author : Stefan Weinzierl
Publisher : Springer Nature
ISBN 13 : 3030995585
Total Pages : 852 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Feynman Integrals by : Stefan Weinzierl

Download or read book Feynman Integrals written by Stefan Weinzierl and published by Springer Nature. This book was released on 2022-06-11 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on Feynman integrals starts from the basics, requiring only knowledge of special relativity and undergraduate mathematics. Feynman integrals are indispensable for precision calculations in quantum field theory. At the same time, they are also fascinating from a mathematical point of view. Topics from quantum field theory and advanced mathematics are introduced as needed. The book covers modern developments in the field of Feynman integrals. Topics included are: representations of Feynman integrals, integration-by-parts, differential equations, intersection theory, multiple polylogarithms, Gelfand-Kapranov-Zelevinsky systems, coactions and symbols, cluster algebras, elliptic Feynman integrals, and motives associated with Feynman integrals. This volume is aimed at a) students at the master's level in physics or mathematics, b) physicists who want to learn how to calculate Feynman integrals (for whom state-of-the-art techniques and computations are provided), and c) mathematicians who are interested in the mathematical aspects underlying Feynman integrals. It is, indeed, the interwoven nature of their physical and mathematical aspects that make Feynman integrals so enthralling.

Representation Theory and Automorphic Forms

Author : Toshiyuki Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 0817646469
Total Pages : 220 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Representation Theory and Automorphic Forms by : Toshiyuki Kobayashi

Download or read book Representation Theory and Automorphic Forms written by Toshiyuki Kobayashi and published by Springer Science & Business Media. This book was released on 2007-10-10 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.

European Congress of Mathematics

Author : Carles Casacuberta
Publisher : Birkhäuser
ISBN 13 : 3034882688
Total Pages : 611 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis European Congress of Mathematics by : Carles Casacuberta

Download or read book European Congress of Mathematics written by Carles Casacuberta and published by Birkhäuser. This book was released on 2012-12-06 with total page 611 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of the proceedings of the third European Congress of Mathematics. Volume I presents the speeches delivered at the Congress, the list of lectures, and short summaries of the achievements of the prize winners as well as papers by plenary and parallel speakers. The second volume collects articles by prize winners and speakers of the mini-symposia. This two-volume set thus gives an overview of the state of the art in many fields of mathematics and is therefore of interest to every professional mathematician. Contributors: R. Ahlswede, V. Bach, V. Baladi, J. Bruna, N. Burq, X. Cabré, P.J. Cameron, Z. Chatzidakis, C. Ciliberto, G. Dal Maso, J. Denef, R. Dijkgraaf, B. Fantechi, H. Föllmer, A.B. Goncharov, A. Grigor'yan, M. Harris, R. Iturriaga, K. Johansson, K. Khanin, P. Koskela, H.W. Lenstra, Jr., F. Loeser, Y.I. Manin, N.S. Manton, Y. Meyer, I. Moerdijk, E.M. Opdam, T. Peternell, B.M.A.G. Piette, A. Reznikov, H. Schlichtkrull, B. Schmidt, K. Schmidt, C. Simó, B. Tóth, E. van den Ban, M.-F. Vignéras, O. Viro.

Linear Differential Equations in the Complex Domain

Author : Yoshishige Haraoka
Publisher : Springer Nature
ISBN 13 : 3030546632
Total Pages : 396 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Linear Differential Equations in the Complex Domain by : Yoshishige Haraoka

Download or read book Linear Differential Equations in the Complex Domain written by Yoshishige Haraoka and published by Springer Nature. This book was released on 2020-11-16 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed introduction to recent developments in the theory of linear differential systems and integrable total differential systems. Starting from the basic theory of linear ordinary differential equations and integrable systems, it proceeds to describe Katz theory and its applications, extending it to the case of several variables. In addition, connection problems, deformation theory, and the theory of integral representations are comprehensively covered. Complete proofs are given, offering the reader a precise account of the classical and modern theory of linear differential equations in the complex domain, including an exposition of Pfaffian systems and their monodromy problems. The prerequisites are a course in complex analysis and the basics of differential equations, topology and differential geometry. This book will be useful for graduate students, specialists in differential equations, and for non-specialists who want to use differential equations.

Analytic Methods In Number Theory: When Complex Numbers Count

Author : Wadim Zudilin
Publisher : World Scientific
ISBN 13 : 9811279330
Total Pages : 192 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Analytic Methods In Number Theory: When Complex Numbers Count by : Wadim Zudilin

Download or read book Analytic Methods In Number Theory: When Complex Numbers Count written by Wadim Zudilin and published by World Scientific. This book was released on 2023-08-22 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no surprise that arithmetic properties of integral ('whole') numbers are controlled by analytic functions of complex variable. At the same time, the values of analytic functions themselves happen to be interesting numbers, for which we often seek explicit expressions in terms of other 'better known' numbers or try to prove that no such exist. This natural symbiosis of number theory and analysis is centuries old but keeps enjoying new results, ideas and methods.The present book takes a semi-systematic review of analytic achievements in number theory ranging from classical themes about primes, continued fractions, transcendence of π and resolution of Hilbert's seventh problem to some recent developments on the irrationality of the values of Riemann's zeta function, sizes of non-cyclotomic algebraic integers and applications of hypergeometric functions to integer congruences.Our principal goal is to present a variety of different analytic techniques that are used in number theory, at a reasonably accessible — almost popular — level, so that the materials from this book can suit for teaching a graduate course on the topic or for a self-study. Exercises included are of varying difficulty and of varying distribution within the book (some chapters get more than other); they not only help the reader to consolidate their understanding of the material but also suggest directions for further study and investigation. Furthermore, the end of each chapter features brief notes about relevant developments of the themes discussed.