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Author : David M. Bressoud
Release : 1950
Genre : Combinatorial identities
Kind : eBook
Book Rating : 272/5 ( reviews)
Book Synopsis Analytic and Combinatorial Generalizations of the Rogers-Ramanujan Identities by : David M. Bressoud
Download or read book Analytic and Combinatorial Generalizations of the Rogers-Ramanujan Identities written by David M. Bressoud. This book was released on 1950. Available in PDF, EPUB and Kindle. Book excerpt:
Author : American Mathematical Society
Release : 1980
Genre : Adams spectral sequences
Kind : eBook
Book Rating : 265/5 ( reviews)
Book Synopsis Analytic and Combinatorial Generalizations of the Rogers-Ramanujan Identities by : American Mathematical Society
Download or read book Analytic and Combinatorial Generalizations of the Rogers-Ramanujan Identities written by American Mathematical Society. This book was released on 1980. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shreejit Bandyopadhyay
Release : 2022
Genre :
Kind : eBook
Book Rating : /5 ( reviews)
Book Synopsis Analytic and Combinatorial Aspects of Certain Identities and Congruences in Partition Theory by : Shreejit Bandyopadhyay
Download or read book Analytic and Combinatorial Aspects of Certain Identities and Congruences in Partition Theory written by Shreejit Bandyopadhyay. This book was released on 2022. 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
Release : 2017-10-16
Genre : Mathematics
Kind : eBook
Book Rating : 962/5 ( reviews)
Book Synopsis An Invitation to the Rogers-Ramanujan Identities by : Andrew V. Sills
Download or read book An Invitation to the Rogers-Ramanujan Identities written by Andrew V. Sills. This book was released on 2017-10-16. 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
Release : 2018-02-01
Genre : Mathematics
Kind : eBook
Book Rating : 764/5 ( reviews)
Book Synopsis Analytic Number Theory, Modular Forms and q-Hypergeometric Series by : George E. Andrews
Download or read book Analytic Number Theory, Modular Forms and q-Hypergeometric Series written by George E. Andrews. This book was released on 2018-02-01. 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.
