Partitions Q Series And Modular Forms

Author : Krishnaswami Alladi,Frank Garvan
Publisher : Springer Science & Business Media
Page : 233 pages
File Size : 51,9 Mb
Release : 2011-11-01
Category : Mathematics
ISBN : 9781461400288

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Partitions, q-Series, and Modular Forms by Krishnaswami Alladi,Frank Garvan Pdf

Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.

Author : Anonim
Publisher : Unknown
Page : 238 pages
File Size : 41,5 Mb
Release : 2011-11-02
Category : Electronic
ISBN : 1461400295

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Partitions, Q-Series, and Modular Forms by Anonim Pdf

Author : Krishnaswami Alladi,Frank Garvan
Publisher : Springer
Page : 224 pages
File Size : 43,7 Mb
Release : 2011-11-01
Category : Mathematics
ISBN : 1461400279

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Partitions, q-Series, and Modular Forms by Krishnaswami Alladi,Frank Garvan Pdf

Partitions, q-Series, and Modular Forms contains a collection of research and survey papers that grew out of a Conference on Partitions, q-Series and Modular Forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions.

Author : George E. Andrews,Frank Garvan
Publisher : Springer
Page : 736 pages
File Size : 48,8 Mb
Release : 2018-02-01
Category : Mathematics
ISBN : 9783319683768

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Analytic Number Theory, Modular Forms and q-Hypergeometric Series by George E. Andrews,Frank Garvan Pdf

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 : Bruce C. Berndt,Ken Ono
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 43,6 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475760446

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Number Theory and Modular Forms by Bruce C. Berndt,Ken Ono Pdf

Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms.

Author : George E. Andrews
Publisher : American Mathematical Soc.
Page : 50 pages
File Size : 51,7 Mb
Release : 1984
Category : Mathematics
ISBN : 9780821823026

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Generalized Frobenius Partitions by George E. Andrews Pdf

This paper is devoted to the study of equilength two-line arrays of non-negative integers. These are called generalized Frobenius partitions. It is shown that such objects have numerous interactions with modular forms, Kloosterman quadratic forms, the Lusztig-Macdonald-Wall conjectures as well as with classical theta functions and additive number theory.

Author : Ken Ono
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 46,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821833681

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The Web of Modularity: Arithmetic of the Coefficients of Modular Forms and $q$-series by Ken Ono Pdf

Chapter 1.

Author : Kathrin Bringmann,Amanda Folsom,Ken Ono,Larry Rolen
Publisher : American Mathematical Soc.
Page : 391 pages
File Size : 45,7 Mb
Release : 2017-12-15
Category : Forms (Mathematics)
ISBN : 9781470419448

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Harmonic Maass Forms and Mock Modular Forms: Theory and Applications by Kathrin Bringmann,Amanda Folsom,Ken Ono,Larry Rolen Pdf

Modular forms and Jacobi forms play a central role in many areas of mathematics. Over the last 10–15 years, this theory has been extended to certain non-holomorphic functions, the so-called “harmonic Maass forms”. The first glimpses of this theory appeared in Ramanujan's enigmatic last letter to G. H. Hardy written from his deathbed. Ramanujan discovered functions he called “mock theta functions” which over eighty years later were recognized as pieces of harmonic Maass forms. This book contains the essential features of the theory of harmonic Maass forms and mock modular forms, together with a wide variety of applications to algebraic number theory, combinatorics, elliptic curves, mathematical physics, quantum modular forms, and representation theory.

Author : George E. Andrews,Bruce C. Berndt
Publisher : Springer
Page : 430 pages
File Size : 55,7 Mb
Release : 2018-09-05
Category : Mathematics
ISBN : 9783319778341

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Ramanujan's Lost Notebook by George E. Andrews,Bruce C. Berndt Pdf

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This fifth and final installment of the authors’ examination of Ramanujan’s lost notebook focuses on the mock theta functions first introduced in Ramanujan’s famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan’s many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. Review from the second volume:"Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited."- MathSciNet Review from the first volume:"Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."- Gazette of the Australian Mathematical Society

Author : Tobias Mühlenbruch,Wissam Raji
Publisher : Springer Nature
Page : 527 pages
File Size : 47,6 Mb
Release : 2020-05-06
Category : Mathematics
ISBN : 9783030404758

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On the Theory of Maass Wave Forms by Tobias Mühlenbruch,Wissam Raji Pdf

This textbook provides a rigorous analytical treatment of the theory of Maass wave forms. Readers will find this unified presentation invaluable, as it treats Maass wave forms as the central area of interest. Subjects at the cutting edge of research are explored in depth, such as Maass wave forms of real weight and the cohomology attached to Maass wave forms and transfer operators. Because Maass wave forms are given a deep exploration, this book offers an indispensable resource for those entering the field. Early chapters present a brief introduction to the theory of classical modular forms, with an emphasis on objects and results necessary to fully understand later material. Chapters 4 and 5 contain the book’s main focus: L-functions and period functions associated with families of Maass wave forms. Other topics include Maass wave forms of real weight, Maass cusp forms, and weak harmonic Maass wave forms. Engaging exercises appear throughout the book, with solutions available online. On the Theory of Maass Wave Forms is ideal for graduate students and researchers entering the area. Readers in mathematical physics and other related disciplines will find this a useful reference as well. Knowledge of complex analysis, real analysis, and abstract algebra is required.

Author : William A. Stein
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 53,8 Mb
Release : 2007-02-13
Category : Mathematics
ISBN : 9780821839607

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Modular Forms, a Computational Approach by William A. Stein Pdf

This marvellous and highly original book fills a significant gap in the extensive literature on classical modular forms. This is not just yet another introductory text to this theory, though it could certainly be used as such in conjunction with more traditional treatments. Its novelty lies in its computational emphasis throughout: Stein not only defines what modular forms are, but shows in illuminating detail how one can compute everything about them in practice. This is illustrated throughout the book with examples from his own (entirely free) software package SAGE, which really bring the subject to life while not detracting in any way from its theoretical beauty. The author is the leading expert in computations with modular forms, and what he says on this subject is all tried and tested and based on his extensive experience. As well as being an invaluable companion to those learning the theory in a more traditional way, this book will be a great help to those who wish to use modular forms in applications, such as in the explicit solution of Diophantine equations. There is also a useful Appendix by Gunnells on extensions to more general modular forms, which has enough in it to inspire many PhD theses for years to come. While the book's main readership will be graduate students in number theory, it will also be accessible to advanced undergraduates and useful to both specialists and non-specialists in number theory. --John E. Cremona, University of Nottingham William Stein is an associate professor of mathematics at the University of Washington at Seattle. He earned a PhD in mathematics from UC Berkeley and has held positions at Harvard University and UC San Diego. His current research interests lie in modular forms, elliptic curves, and computational mathematics.

Author : Greville G. Corbett,Norman M. Fraser,Scott McGlashan
Publisher : Cambridge University Press
Page : 364 pages
File Size : 41,5 Mb
Release : 1993-06-24
Category : Language Arts & Disciplines
ISBN : 052140245X

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Heads in Grammatical Theory by Greville G. Corbett,Norman M. Fraser,Scott McGlashan Pdf

A study of the idea of the 'head' or dominating element of a phrase.

Author : Andrew V. Sills
Publisher : CRC Press
Page : 257 pages
File Size : 52,8 Mb
Release : 2017-10-16
Category : Mathematics
ISBN : 9781351647960

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An Invitation to the Rogers-Ramanujan Identities by Andrew V. Sills Pdf

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 : James Mc Laughlin
Publisher : World Scientific
Page : 400 pages
File Size : 42,5 Mb
Release : 2017-09-22
Category : Mathematics
ISBN : 9789813223387

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Topics and Methods in q-Series by James Mc Laughlin Pdf

The book provides a comprehensive introduction to the many aspects of the subject of basic hypergeometric series. The book essentially assumes no prior knowledge but eventually provides a comprehensive introduction to many important topics. After developing a treatment of historically important topics such as the q-binomial theorem, Heine's transformation, the Jacobi triple product identity, Ramanujan's 1-psi-1 summation formula, Bailey's 6-psi-6 summation formula and the Rogers-Fine identity, the book goes on to delve more deeply into important topics such as Bailey- and WP-Bailey pairs and chains, q-continued fractions, and mock theta functions. There are also chapters on other topics such as Lambert series and combinatorial proofs of basic hypergeometric identities. The book could serve as a textbook for the subject at the graduate level and as a textbook for a topic course at the undergraduate level (earlier chapters). It could also serve as a reference work for researchers in the area.

Author : Ae Ja Yee,
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 45,8 Mb
Release : 2014-10-14
Category : Mathematics
ISBN : 9781470410780

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Ramanujan 125 by Ae Ja Yee, Pdf

This volume contains the proceedings of an international conference to commemorate the 125th anniversary of Ramanujan's birth, held from November 5-7, 2012, at the University of Florida, Gainesville, Florida. Srinivasa Ramanujan was India's most famous mathematician. This volume contains research and survey papers describing recent and current developments in the areas of mathematics influenced by Ramanujan. The topics covered include modular forms, mock theta functions and harmonic Maass forms, continued fractions, partition inequalities, -series, representations of affine Lie algebras and partition identities, highly composite numbers, analytic number theory and quadratic forms.