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001 978-1-4614-0028-8
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007 cr nn 008mamaa
008 111031s2012 xxu| s |||| 0|eng d
020 _a9781461400288
_9978-1-4614-0028-8
024 7 _a10.1007/978-1-4614-0028-8
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aAlladi, Krishnaswami.
_eeditor.
245 1 0 _aPartitions, q-Series, and Modular Forms
_h[electronic resource] /
_cedited by Krishnaswami Alladi, Frank Garvan.
264 1 _aNew York, NY :
_bSpringer New York,
_c2012.
300 _aXII, 224 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aDevelopments in Mathematics,
_x1389-2177 ;
_v23
505 0 _a-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).            .
520 _aThis 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.
650 0 _aMathematics.
650 0 _aFunctions, special.
650 0 _aCombinatorics.
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
650 2 4 _aCombinatorics.
650 2 4 _aSpecial Functions.
700 1 _aGarvan, Frank.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461400271
830 0 _aDevelopments in Mathematics,
_x1389-2177 ;
_v23
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-0028-8
912 _aZDB-2-SMA
999 _c100797
_d100797