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Author : David M. Bressoud
Publisher :
ISBN 13 : 9780821822272
Total Pages : 54 pages
Book Rating : 4.8/5 (222 download)
Download or read book Analytic and Combinatorial Generalizations of the Rogers-Ramanujan Identities written by David M. Bressoud and published by . This book was released on 1950 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : American Mathematical Society
Publisher :
ISBN 13 : 9780821822265
Total Pages : 130 pages
Book Rating : 4.8/5 (222 download)
Download or read book Analytic and Combinatorial Generalizations of the Rogers-Ramanujan Identities written by American Mathematical Society and published by . This book was released on 1980 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shreejit Bandyopadhyay
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)
Download or read book Analytic and Combinatorial Aspects of Certain Identities and Congruences in Partition Theory written by Shreejit Bandyopadhyay and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation explores three related topics in the theory of integer partitions. We first revisit certain conjectures made by George Beck about the crank of a partition. We discuss a new approach to these conjectures by decomposing the relevant crank generating function and further explore connections with certain identities involving generalized Lambert series and Appell-Lerch sums. After that, we derive certain weighted generating functions of cranks by both analytic and combinatorial arguments. Lastly, we consider overpartition analogues for Bressoud's generalizations of the famous Rogers-Ramanujan identities. We discuss some new Rogers-Ramanujan type overpartition identities under certain constraints on odd and even parts of the partitions.
Author : Andrew V. Sills
Publisher : CRC Press
ISBN 13 : 1351647962
Total Pages : 263 pages
Book Rating : 4.3/5 (516 download)
Download or read book An Invitation to the Rogers-Ramanujan Identities written by Andrew V. Sills and published by CRC Press. This book was released on 2017-10-16 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere.
Author : George E. Andrews
Publisher : Springer
ISBN 13 : 3319683764
Total Pages : 764 pages
Book Rating : 4.3/5 (196 download)
Download or read book Analytic Number Theory, Modular Forms and q-Hypergeometric Series written by George E. Andrews and published by Springer. This book was released on 2018-02-01 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory. Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find this volume a valuable resource on new developments in various aspects of number theory.
Author : Krishnaswami Alladi
Publisher : Springer
ISBN 13 : 3540466819
Total Pages : 240 pages
Book Rating : 4.5/5 (44 download)
Download or read book Number Theory, Madras 1987 written by Krishnaswami Alladi and published by Springer. This book was released on 2006-11-14 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Robin Wilson
Publisher :
ISBN 13 : 0199656592
Total Pages : 392 pages
Book Rating : 4.1/5 (996 download)
Download or read book Combinatorics: Ancient & Modern written by Robin Wilson and published by . This book was released on 2013-06-27 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics is the branch of discrete mathematics that studies (and counts) permutations, combinations, and arrangements of sets of elements. This book constitutes the first book-length survey of the history of combinatorics and uniquely assembles research in the area that would otherwise be inaccessible to the general reader.
Author : Eric M. Rains
Publisher : American Mathematical Soc.
ISBN 13 : 1470446901
Total Pages : 115 pages
Book Rating : 4.4/5 (74 download)
Download or read book Bounded Littlewood Identities written by Eric M. Rains and published by American Mathematical Soc.. This book was released on 2021-07-21 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe a method, based on the theory of Macdonald–Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald’s partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R, S) in terms of ordinary Macdonald polynomials, are q, t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups. In the classical limit, our method implies that MacMahon’s famous ex-conjecture for the generating function of symmetric plane partitions in a box follows from the identification of GL(n, R), O(n) as a Gelfand pair. As further applications, we obtain combinatorial formulas for characters of affine Lie algebras; Rogers–Ramanujan identities for affine Lie algebras, complementing recent results of Griffin et al.; and quadratic transformation formulas for Kaneko–Macdonald-type basic hypergeometric series.
Author : Warren P. Johnson
Publisher : American Mathematical Soc.
ISBN 13 : 1470456230
Total Pages : 519 pages
Book Rating : 4.4/5 (74 download)
Download or read book An Introduction to q-analysis written by Warren P. Johnson and published by American Mathematical Soc.. This book was released on 2020-10-06 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to q q-analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view. The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for self-study in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.
Author : George E. Andrews
Publisher : Cambridge University Press
ISBN 13 : 9780521637664
Total Pages : 274 pages
Book Rating : 4.6/5 (376 download)
Download or read book The Theory of Partitions written by George E. Andrews and published by Cambridge University Press. This book was released on 1998-07-28 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses mathematics related to partitions of numbers into sums of positive integers.
Author : Mourad E. H. Ismail
Publisher : Springer Science & Business Media
ISBN 13 : 0387242333
Total Pages : 497 pages
Book Rating : 4.3/5 (872 download)
Download or read book Theory and Applications of Special Functions written by Mourad E. H. Ismail and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of articles on various aspects of q-series and special functions dedicated to Mizan Rahman. It also includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject.
Author : Pradip Debnath
Publisher : World Scientific
ISBN 13 : 9811272611
Total Pages : 463 pages
Book Rating : 4.8/5 (112 download)
Download or read book Advances In Number Theory And Applied Analysis written by Pradip Debnath and published by World Scientific. This book was released on 2023-05-08 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presently, the exploration of the applications of different techniques and tools of number theory and mathematical analysis are extensively prevalent in various areas of engineering, mathematical, physical, biological and statistical sciences. This book will present the most recent developments in these two fields through contributions from eminent scientists and mathematicians worldwide.The book will present the current state of the art development in these two areas through original new contributions and surveys. As such, readers will find several useful tools and techniques to develop their skills and expertise in number theory and applied analysis. New research directions are also indicated in each of the chapters. This book is meant for graduate students, faculty and researchers willing to expand their knowledge in number theory and mathematical analysis. The readers of this book will require minimum prerequisites of analysis, topology, number theory and functional analysis.
Author : Richard Askey
Publisher : American Mathematical Soc.
ISBN 13 : 0821823213
Total Pages : 63 pages
Book Rating : 4.8/5 (218 download)
Download or read book Some Basic Hypergeometric Orthogonal Polynomials that Generalize Jacobi Polynomials written by Richard Askey and published by American Mathematical Soc.. This book was released on 1985 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: A very general set of orthogonal polynomials in one variable that extends the classical polynomials is a set we called the q-Racah polynomials. In an earlier paper we gave the orthogonality relation for these polynomials when the orthogonality is purely discrete. We now give the weight function in the general case and a number of other properties of these very interesting orthogonal polynomials.
Author : Stephen Berman
Publisher : American Mathematical Soc.
ISBN 13 : 0821827162
Total Pages : 346 pages
Book Rating : 4.8/5 (218 download)
Download or read book Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory written by Stephen Berman and published by American Mathematical Soc.. This book was released on 2002 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Because of its many applications to mathematics and mathematical physics, the representation theory of infinite-dimensional Lie and quantized enveloping algebras comprises an important area of current research. This volume includes articles from the proceedings of an international conference, ``Infinite-Dimensional Lie Theory and Conformal Field Theory'', held at the University of Virginia. Many of the contributors to the volume are prominent researchers in the field. Thisconference provided an opportunity for mathematicians and physicists to interact in an active research area of mutual interest. The talks focused on recent developments in the representation theory of affine, quantum affine, and extended affine Lie algebras and Lie superalgebras. They also highlightedapplications to conformal field theory, integrable and disordered systems. Some of the articles are expository and accessible to a broad readership of mathematicians and physicists interested in this area; others are research articles that are appropriate for more advanced readers.
Author : D. Winter
Publisher : Springer
ISBN 13 : 3540392629
Total Pages : 243 pages
Book Rating : 4.5/5 (43 download)
Download or read book Lie Algebras and Related Topics written by D. Winter and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bruce C. Berndt
Publisher : Springer Science & Business Media
ISBN 13 : 146120965X
Total Pages : 521 pages
Book Rating : 4.4/5 (612 download)
Download or read book Ramanujan’s Notebooks written by Bruce C. Berndt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: Upon Ramanujans death in 1920, G. H. Hardy strongly urged that Ramanujans notebooks be published and edited. In 1957, the Tata Institute of Fundamental Research in Bombay finally published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the task of editing Ramanujans notebooks: proofs are provided to theorems not yet proven in previous literature, and many results are so startling as to be unique.
Author : Georgia Benkart
Publisher : American Mathematical Soc.
ISBN 13 : 0821851195
Total Pages : 352 pages
Book Rating : 4.8/5 (218 download)
Download or read book Lie Algebras and Related Topics written by Georgia Benkart and published by American Mathematical Soc.. This book was released on 1990 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This book includes topics such as Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras.
