Harmonic Maass Forms And Mock Modular Forms Theory And Applications

Author by : Kathrin Bringmann
Language : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 59
Total Download : 313
File Size : 50,6 Mb
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Description : 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.


Harmonic Maass Forms And Mock Modular Forms Theory And Applications

Author by : Kathrin Bringmann
Language : en
Publisher by : American Mathematical Soc.
Format Available : PDF, ePub, Mobi
Total Read : 94
Total Download : 597
File Size : 43,6 Mb
pdf pdf

Description : 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.


Ramanujan S Lost Notebook

Author by : George E. Andrews
Language : en
Publisher by : Springer
Format Available : PDF, ePub, Mobi
Total Read : 82
Total Download : 849
File Size : 43,8 Mb
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Description :


An Invitation To The Rogers Ramanujan Identities

Author by : Andrew V. Sills
Language : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 81
Total Download : 99
File Size : 52,5 Mb
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Description : 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.


From Fourier Analysis And Number Theory To Radon Transforms And Geometry

Author by : Hershel M. Farkas
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 98
Total Download : 791
File Size : 49,5 Mb
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Description : ​​​A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.​A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.


Partitions Q Series And Modular Forms

Author by : Krishnaswami Alladi
Language : en
Publisher by : Springer Science & Business Media
Format Available : PDF, ePub, Mobi
Total Read : 89
Total Download : 318
File Size : 41,8 Mb
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Description : 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.


Interplay Between Weak Maass Forms And Modular Forms And Statistical Properties Of Number Theoretic Objects

Author by : Robert C. Rhoades
Language : en
Publisher by : ProQuest
Format Available : PDF, ePub, Mobi
Total Read : 92
Total Download : 622
File Size : 48,8 Mb
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Description : This work begins by systematically providing identities connecting Ramanujan's mock theta functions with classical modular forms. Such results are possible because of cancelation among the non-holomorphic parts of different harmonic weak Maass forms.


Reviews In Number Theory 1984 96

Author by :
Language : en
Publisher by : Amer Mathematical Society
Format Available : PDF, ePub, Mobi
Total Read : 17
Total Download : 834
File Size : 41,8 Mb
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Description : These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.