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Generalized Frobenius Partitions

1984 Mathematics
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Release : 1984
Genre : Mathematics
Kind : eBook
Book Rating : 027/5 ( reviews)

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Book Synopsis Generalized Frobenius Partitions by : George E. Andrews

Download or read book Generalized Frobenius Partitions written by George E. Andrews. This book was released on 1984. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Q-series

1986-01-01 Mathematics
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Release : 1986-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 114/5 ( reviews)

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Book Synopsis Q-series by : George E. Andrews

Download or read book Q-series written by George E. Andrews. This book was released on 1986-01-01. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to q-analysis

2020-10-06 Education
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Release : 2020-10-06
Genre : Education
Kind : eBook
Book Rating : 230/5 ( reviews)

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Book Synopsis An Introduction to q-analysis by : Warren P. Johnson

Download or read book An Introduction to q-analysis written by Warren P. Johnson. This book was released on 2020-10-06. Available in PDF, EPUB and Kindle. Book excerpt: Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to q q-analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view. The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for self-study in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.

Analytic Number Theory, Modular Forms and q-Hypergeometric Series

2018-02-01 Mathematics
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Release : 2018-02-01
Genre : Mathematics
Kind : eBook
Book Rating : 764/5 ( reviews)

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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.

Basic Hypergeometric Series and Applications

1988 Mathematics
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Release : 1988
Genre : Mathematics
Kind : eBook
Book Rating : 245/5 ( reviews)

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Book Synopsis Basic Hypergeometric Series and Applications by : Nathan Jacob Fine

Download or read book Basic Hypergeometric Series and Applications written by Nathan Jacob Fine. This book was released on 1988. Available in PDF, EPUB and Kindle. Book excerpt: The theory of partitions, founded by Euler, has led in a natural way to the idea of basic hypergeometric series, also known as Eulerian series. These series were first studied systematically by Heine, but many early results are attributed to Euler, Gauss, and Jacobi. This book provides a simple approach to basic hypergeometric series.

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