Автор: Cooper Shaun Et Al Название: Development Of Elliptic Functions According To Ramanujan ISBN: 9814366455 ISBN-13(EAN): 9789814366458 Издательство: World Scientific Publishing Рейтинг: Цена: 74970.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Provides an efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. This book is suitable for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan`s work.
Автор: Cooper Shaun Название: Ramanujan`s Theta Functions ISBN: 3319858432 ISBN-13(EAN): 9783319858432 Издательство: Springer Рейтинг: Цена: 149060.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Preface.- 0. Sum to Product Identities.- 1. Elliptic Functions.- 2. Transformations.- 3. Theta Functions.- 4. Levels 1, 2, 3, and 4: Jacobi's Inversion Theorem and Ramanujan's Alternative Theories.- 5. Level 5: The Rogers-Ramanujan Continued Fraction.- 6. Level 6: Ramanujan's Cubic Continued Fraction.- 7. Level 7.- 8. Level 8: The Ramanujan-Gollnitz-Gordon Continued Fraction.- 9. Level 9.- 10. Level 10: Ramanujan's Function k.- 11. Levels 11 and 23.- 12. Level 12.- 13. Hypergeometric Modular Transformations.- 14. Ramanujan's Series for 1/pi.- References.
Автор: Sills, Andrew V. Название: Invitation to the rogers-ramanujan identities ISBN: 0367657619 ISBN-13(EAN): 9780367657611 Издательство: Taylor&Francis Рейтинг: Цена: 51030.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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.
Автор: Davidoff Название: Elementary Number Theory, Group Theory and Ramanujan Graphs ISBN: 0521824265 ISBN-13(EAN): 9780521824262 Издательство: Cambridge Academ Рейтинг: Цена: 160510.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This text is a self contained treatment of expander graphs and in particular their explicit construction. Expander graphs are both highly connected but sparse, and besides their interest within combinatorics and graph theory, they also find various applications in computer science and engineering.
Автор: M. Ram Murty; V. Kumar Murty Название: The Mathematical Legacy of Srinivasa Ramanujan ISBN: 8132217438 ISBN-13(EAN): 9788132217435 Издательство: Springer Рейтинг: Цена: 107130.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Focusing on a subset of Ramanujan`s significant papers, this book gives an informal account of major developments that emanated from his work in the 20th and 21st centuries. The essays presented here show how Ramanujan shaped the course of modern mathematics.
Автор: Bernard Candelpergher Название: Ramanujan Summation of Divergent Series ISBN: 3319636294 ISBN-13(EAN): 9783319636290 Издательство: Springer Рейтинг: Цена: 41920.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This provides simple proofs of theorems on the summation of some divergent series. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes.
Автор: Bruce C. Berndt Название: Ramanujan`s Notebooks ISBN: 1461270073 ISBN-13(EAN): 9781461270072 Издательство: Springer Рейтинг: Цена: 186330.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Srinivasa Ramanujan is, arguably, the greatest mathematicianthat India has produced. He died very young, at the age of 32,leaving behind three notebooks containing almost 3000theorems, virtually all without proof. Hardy andothers strongly urged that notebooks be edited andpublished, and the result is this series of books.
Автор: Bruce C. Berndt Название: Ramanujan`s Notebooks ISBN: 1461269636 ISBN-13(EAN): 9781461269632 Издательство: Springer Рейтинг: Цена: 232910.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In 1957, the Tata Institute of Fundamental Research in Bombay finally published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the task of editing Ramanujans notebooks: proofs are provided to theorems not yet proven in previous literature, and many results are so startling as to be unique.
Автор: Bruce C. Berndt Название: Ramanujan`s Notebooks ISBN: 1461288657 ISBN-13(EAN): 9781461288657 Издательство: Springer Рейтинг: Цена: 153720.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: During the years 1903-1914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Part I, published in 1985, contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujan`s quarterly reports. In this volume, we examine Chapters 10-15 in Ramanujan`s second notebook.
Автор: Krishnaswami Alladi Название: Number Theory, Madras 1987 ISBN: 354051595X ISBN-13(EAN): 9783540515951 Издательство: Springer Рейтинг: Цена: 41920.00 T Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Srinivasa Rao K. Название: Srinivasa Ramanujan: Life and Work of a Natural Mathematical Genius, Swayambhu ISBN: 9811604460 ISBN-13(EAN): 9789811604461 Издательство: Springer Цена: 111790.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Sharing valuable insights into the many stages of Ramanujan`s life, this book provides glimpses into his prolific research on highly composite numbers, partitions, continued fractions, mock theta functions, arithmetic, and hypergeometric functions which led the author to discover a new summation theorem.
In this monograph, we study recent results on some categories of trigonometric/exponential sums along with various of their applications in Mathematical Analysis and Analytic Number Theory. Through the two chapters of this monograph, we wish to highlight the applicability and breadth of techniques of trigonometric/exponential sums in various problems focusing on the interplay of Mathematical Analysis and Analytic Number Theory. We wish to stress the point that the goal is not only to prove the desired results, but also to present a plethora of intermediate Propositions and Corollaries investigating the behaviour of such sums, which can also be applied in completely different problems and settings than the ones treated within this monograph.
In the present work we mainly focus on the applications of trigonometric/exponential sums in the study of Ramanujan sums - which constitute a very classical domain of research in Number Theory - as well as the study of certain cotangent sums with a wide range of applications, especially in the study of Dedekind sums and a facet of the research conducted on the Riemann Hypothesis. For example, in our study of the cotangent sums treated within the second chapter, the methods and techniques employed reveal unexpected connections with independent and very interesting problems investigated in the past by R de la Bretиche and G Tenenbaum on trigonometric series, as well as by S Marmi, P Moussa and J-C Yoccoz on Dynamical Systems.
Overall, a reader who has mastered fundamentals of Mathematical Analysis, as well as having a working knowledge of Classical and Analytic Number Theory, will be able to gradually follow all the parts of the monograph. Therefore, the present monograph will be of interest to advanced undergraduate and graduate students as well as researchers who wish to be informed on the latest developments on the topics treated.
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