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＜電子ブック＞
Partitions, q-Series, and Modular Forms / edited by Krishnaswami Alladi, Frank Garvan
(Developments in Mathematics. ISSN:2197795X ; 23)

版	1st ed. 2012.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2012
本文言語	英語
大きさ	XII, 224 p : online resource
著者標目	Alladi, Krishnaswami editor Garvan, Frank editor SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Discrete mathematics LCSH:Special functions FREE:Number Theory FREE:Discrete Mathematics FREE:Special Functions
一般注記	-Preface (K. Alladi and F. Garvan) -- 1. MacMahon's dream (G. E. Andrews and P. Paule) -- 2. Ramanujan's elementary method in partition congruences (B. Berndt, C. Gugg, and S. Kim) -- 3. Coefficients of harmonic Maass forms (K. Bringmann and K. Ono) -- 4. On the growth of restricted partition functions (E. R. Canfield and H. Wilf) -- 5. On applications of roots of unity to product identities (Z. Cao) -- 6. Lecture hall sequences, q-series, and asymmetric partition identities (S. Corteel, C. Savage and A. Sills) -- 7. Generalizations of Hutchinson's curve and the Thomae formula (H. Farkas) -- 8. On the parity of the Rogers-Ramanujan coefficients (B. Gordon) -- 9. A survey of the classical mock theta functions (B. Gordon and R. McIntosh) -- 10. An application of the Cauchy-Sylvester theorem on compound determinants to a BC_n Jackson integral (M. Ito and S. Okada) -- 11. Multiple generalizations of q-series identities found in Ramanujan's Lost Notebook (Y. Kajihara) -- 12. Non-terminating q-Whipple transformations for basic hypergeometric series in U(n) (S. C. Milne and J. W. Newcomb).             This book contains a unique collection of both research and survey papers written by an international group of some of the world's experts on partitions, q-series, and modular forms, as outgrowths of a conference held at the University of Florida, Gainesville in March 2008. The success of this conference has led to annual year-long programs in Algebra, Number Theory, and Combinatorics (ANTC) at the university. A common theme in the book is the study of q-series, an area which in recent years has witnessed dramatic advances having significant impact on a variety of fields within and outside of mathematics such as physics. Most major aspects of the modern theory of q-series and how they relate to number theory, combinatorics, and special functions are represented in this volume. Topics include the theory of partitions via computer algebra, elementary asymptotic methods; expositions on Ramanujan's mock theta-functions emphasizing the classical aspects as well as the recent exciting connections with the theory of harmonic Maass forms; congruences for modular forms; a study of theta-functions from elementary, function-theoretic and Riemann surface viewpoints; and a systematic analysis of multiple basic hypergeometric functions associated with root systems of Lie algebras.  The broad range of topics covered in this volume will be of interest to both researchers and graduate students who want to learn of recent developments in the theory of partitions, q-series and modular forms and their far reaching impact on diverse areas of mathematics HTTP:URL=https://doi.org/10.1007/978-1-4614-0028-8

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