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Ramanujan's Theta Functions
Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.
Only a Mate's Touch
Only two who are truly destined for one another will find a way to stitch together the ragged edges of their souls and become complete. Shaun has been perpetually unlucky in love. None of the women he meets are his mate...but that doesn't stop him from finding enjoyment with those he becomes close to. All that changes on the day he meets Meeghan Nicholson, a new deputy for the town of Stonepass. Shaun recognises that the feisty black-haired beauty is the one he's been searching for all his life. So it's a shame that the woman hates him on first sight. Now a man who's always been known to speak before he thinks must sweet talk his way into his mate's arms. Meeghan is tired of men who think that because she's a woman they can get her to do whatever they want. Her body might soften at Shaun Colfer's seductive touch, but she refuses to let her heart succumb to the sneaky shifter. Can Meeghan calm Shaun's tempestuousness? Can Shaun crack the shell surrounding Meeghan's heart? It just might work...but only with a mate's touch.
The Taste of Devotion
One man searching for a place to call home stumbles into the arms of another wishing for a mate to complete his. Cooper Tessen, enforcer for the Phantom River Pack and Sheriff of Stonepass, has watched each of his two best friends enjoy their mated bliss. He's thrilled they've found happiness, however, he feels a distance growing between him and his blood brothers because he has no experience of the connection between a shifter and his mate. Cooper fills the hours of his lonely days by spending as much time as possible working at the station to protect his town, and, secretly, off on dangerous missions for the government. Burning the candle at both ends gives him little time to focus on his ...
Development of Elliptic Functions According to Ramanujan
This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter. The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan's work. It can be read by anyone with some undergraduate knowledge of real and complex analysis.
An Introduction to q-analysis
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.
Topics in Complex Analysis
Complex analysis is found in many areas of applied mathematics, from fluid mechanics, thermodynamics, signal processing, control theory, mechanical and electrical engineering to quantum mechanics, among others. And of course, it is a fundamental branch of pure mathematics. The coverage in this text includes advanced topics that are not always considered in more elementary texts. These topics include, a detailed treatment of univalent functions, harmonic functions, subharmonic and superharmonic functions, Nevanlinna theory, normal families, hyperbolic geometry, iteration of rational functions, and analytic number theory. As well, the text includes in depth discussions of the Dirichlet Problem, Green’s function, Riemann Hypothesis, and the Laplace transform. Some beautiful color illustrations supplement the text of this most elegant subject.
Special Functions, $q$-Series and Related Topics
This book contains contributions from the proceedings at The Fields Institute workshop on Special Functions, q-Series and Related Topics that was held in June 1995. The articles cover areas from quantum groups and their representations, multivariate special functions, q-series, and symbolic algebra techniques as well as the traditional areas of single-variable special functions. The book contains both pure and applied topics and reflects recent trends of research in the various areas of special functions.
Transcendence in Algebra, Combinatorics, Geometry and Number Theory
This proceedings volume gathers together original articles and survey works that originate from presentations given at the conference Transient Transcendence in Transylvania, held in Brașov, Romania, from May 13th to 17th, 2019. The conference gathered international experts from various fields of mathematics and computer science, with diverse interests and viewpoints on transcendence. The covered topics are related to algebraic and transcendental aspects of special functions and special numbers arising in algebra, combinatorics, geometry and number theory. Besides contributions on key topics from invited speakers, this volume also brings selected papers from attendees.
Enterprise Information Systems
This book contains substantially extended and revised versions of the best papers from the 15th International Conference on Enterprise Information Systems, ICEIS 2013, held in Angers, France, in July 2013. The 29 full and two invited papers included in this volume were carefully reviewed and selected from 321 submissions. They reflect state-of-the-art research focusing mainly on real-world applications and highlight the benefits of information systems and technology for industry and services, thus connecting academia with the world of real enterprises. The topics covered are: databases and information systems integration, artificial intelligence and decision support systems, information systems analysis and specification, software agents and Internet computing, human–computer interaction, and enterprise architecture.
Analytic Number Theory, Modular Forms and q-Hypergeometric Series
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.
