Search Results: ramanujan-s-lost-notebook-part-i-pt-1

Ramanujan's Lost Notebook

Author: George E. Andrews,Bruce C. Berndt

Publisher: Springer Science & Business Media

ISBN: 1461440815

Category: Mathematics

Page: 439

View: 2433

​​​​In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This volume is the fourth of five volumes that the authors plan to write on Ramanujan’s lost notebook.​ In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series. Most of the entries examined in this volume fall under the purviews of number theory and classical analysis. Several incomplete manuscripts of Ramanujan published by Narosa with the lost notebook are discussed. Three of the partial manuscripts are on diophantine approximation, and others are in classical Fourier analysis and prime number theory. Most of the entries in number theory fall under the umbrella of classical analytic number theory. Perhaps the most intriguing entries are connected with the classical, unsolved circle and divisor problems. Review from the second volume: "Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited." - MathSciNet Review from the first volume: "Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete." - Gazette of the Australian Mathematical Society​

Ramanujan’s Notebooks

Author: Bruce C. Berndt

Publisher: Springer Science & Business Media

ISBN: 1461208793

Category: Mathematics

Page: 451

View: 1653

During the years 1903-1914, Ramanujan worked in almost complete isolation in India. During this time, he recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature, most were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit Ramanujan's notebooks, but they never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the fourth of five volumes devoted to the editing of Ramanujan's notebooks. Parts I, II, and III, published in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in Ramanujan's second notebook as well as a description of his quarterly reports. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the notebooks are new. Many of them are so startling and different that there are no results akin to them in the literature.

Surveys in Number Theory

Author: Krishnaswami Alladi

Publisher: Springer Science & Business Media

ISBN: 0387785108

Category: Mathematics

Page: 188

View: 6722

Number theory has a wealth of long-standing problems, the study of which over the years has led to major developments in many areas of mathematics. This volume consists of seven significant chapters on number theory and related topics. Written by distinguished mathematicians, key topics focus on multipartitions, congruences and identities (G. Andrews), the formulas of Koshliakov and Guinand in Ramanujan's Lost Notebook (B. C. Berndt, Y. Lee, and J. Sohn), alternating sign matrices and the Weyl character formulas (D. M. Bressoud), theta functions in complex analysis (H. M. Farkas), representation functions in additive number theory (M. B. Nathanson), and mock theta functions, ranks, and Maass forms (K. Ono), and elliptic functions (M. Waldschmidt).

Number Theoretic Methods

Future Trends

Author: Shigeru Kanemitsu,Chaohua Jia

Publisher: Springer Science & Business Media

ISBN: 1475736754

Category: Mathematics

Page: 441

View: 5749

This volume contains the proceedings of the very successful second China-Japan Seminar held in lizuka, Fukuoka, Japan, during March 12-16, 2001 under the support of the Japan Society for the Promotion of Science (JSPS) and the National Science Foundation of China (NSFC), and some invited papers of eminent number-theorists who visited Japan during 1999-2001 at the occasion of the Conference at the Research Institute of Mathematical Sciences (RIMS), Kyoto University. The proceedings of the 1st China-Japan Seminar held in September 1999 in Beijing has been published recently {2002) by Kluwer as DEVM 6 which also contains some invited papers. The topics of that volume are, however, restricted to analytic number theory and many papers in this field are assembled. In this volume, we return to the lines of the previous one "Number Theory and its Applications", published as DEVM 2 by Kluwer in 1999 and uphold the spirit of presenting various topics in number theory and related areas with possible applica tions, in a unified manner, and this time in nearly a book form with a well-prepared index. We accomplish this task by collecting highly informative and readable survey papers (including half-survey type papers), giving overlooking surveys of the hith erto obtained results in up-to-the-hour form with insight into the new developments, which are then analytically continued to a collection of high standard research papers which are concerned with rather diversed areas and will give good insight into new researches in the new century.

Der das Unendliche kannte

Das Leben des genialen Mathematikers Srinivasa Ramanujan

Author: Robert Kanigel

Publisher: Springer-Verlag

ISBN: 3322837696

Category: Science

Page: 331

View: 1138

Die Lehre von den Kettenbrüchen (Classic Reprint)

Author: Oskar Perron

Publisher: Forgotten Books

ISBN: 9781390988550

Category: Mathematics

Page: 542

View: 4262

Excerpt from Die Lehre von den Kettenbrüchen Darstellung doch viel mehr auf bereits Gefundenes zu stützen in der Lage bin. Sehr oft tritt aber auch eine Formel ziemlich unerwartet in einem bisher nicht bemerkten Zusammenhang auf. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Mathematical Reviews

Author: N.A

Publisher: N.A


Category: Mathematics

Page: N.A

View: 8764

Charlemagne and his heritage

Author: Paul Leo Butzer,Walter Oberschelp

Publisher: Brepols Publishers


Category: Civilization, Medieval

Page: 571

View: 1409


Algorithmen, Computer, Arithmetik

Author: Jörg Arndt,Christoph Haenel

Publisher: Springer-Verlag

ISBN: 366209360X

Category: Computers

Page: 264

View: 8648

Eine kleine Geschichte der Unendlichkeit

Author: Brian Clegg

Publisher: Rowohlt Verlag GmbH

ISBN: 364404371X

Category: Fiction

Page: 352

View: 4648

Philosophen und Mathematiker hat das Nachsinnen über das Wesen des Unendlichen buchstäblich den Verstand geraubt – und dennoch ist es ein Konzept, das immer wieder unser Leben bestimmt. In diesem mit Anekdoten und Geschichten gespickten Buch nimmt uns Brian Clegg mit auf eine Reise durch das Grenzland zwischen dem extrem Großen und dem Ultimativen, von Archimedes, der die Zahl der Sandkörner bestimmte, die das Universum füllen würden, bis zu den neuesten Theorien über die physikalische Realität des Unendlichen.

Reviews in Number Theory, 1984-96

As Printed in Mathematical Reviews

Author: N.A

Publisher: Amer Mathematical Society

ISBN: 9780821809310

Category: Mathematics

Page: 405

View: 703

These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews between 1984 and 1996. This is the third such set of volumes in number theory. The first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.

Collected papers

Author: Emil Artin

Publisher: Springer


Category: Mathematics

Page: 560

View: 1195

Liebe und Mathematik

Im Herzen einer verborgenen Wirklichkeit

Author: Edward Frenkel

Publisher: Springer-Verlag

ISBN: 3662434210

Category: Mathematics

Page: 317

View: 6823

Geometrie der Zahlen

Author: Hermann Minkowski

Publisher: N.A

ISBN: 9783738705706


Page: 268

View: 1538


Author: N.A

Publisher: N.A


Category: Academic libraries

Page: N.A

View: 9606

Reviews in Number Theory 1973-83

As Printed in Mathematical Reviews

Author: Richard K. Guy

Publisher: American Mathematical Society(RI)


Category: Mathematical reviews

Page: 477

View: 6578

Untersuchungen über höhere Arithmetik

Author: Carl Friedrich Gauss

Publisher: American Mathematical Soc.

ISBN: 0821842137

Category: Mathematics

Page: 695

View: 1764

In this volume are included all of Gauss's number-theoretic works: his masterpiece, Disquisitiones Arithmeticae, published when Gauss was only 25 years old; several papers published during the ensuing 31 years; and papers taken from material found in Gauss's handwriting after his death. These papers include a fourth, fifth, and sixth proof of the Quadratic Reciprocity Law, researches on biquadratic residues, quadratic forms, and other topics. This reprint of the German translation from Latin of the second edition published in 1889 includes an extensive appendix and concludes with a commentary on the papers (with references, where appropriate, to the relevant pages of the Disquisitiones).

Elektronen und Chemische Bindung

Author: Harry B. Gray

Publisher: Walter de Gruyter

ISBN: 3110830620

Category: Reference

Page: 205

View: 4215

“Electrons and chemical bonding: This standard textbook on quantum chemistry is easy to understand even for chemists; its basic concepts never become obsolete. Well done didactically, concise and to-the-point.” Prof. Dr. Ralf Steudel, TU Berlin

Leading Change

Wie Sie Ihr Unternehmen in acht Schritten erfolgreich verändern

Author: John P. Kotter

Publisher: Vahlen

ISBN: 3800646153

Category: Fiction

Page: 158

View: 7434

John P. Kotters wegweisendes Werk Leading Change erschien 1996 und zählt heute zu den wichtigsten Managementbüchern überhaupt. Es wurde in zahlreiche Sprachen übersetzt und millionenfach verkauft. Der Druck auf Unternehmen, sich den permanent wandelnden internen und externen Einflüssen zu stellen, wird weiter zunehmen. Dabei gehört ein offener, aber professionell geführter Umgang mit Change-Prozessen zu den Wesensmerkmalen erfolgreicher Unternehmen im 21. Jahrhundert und zu den größten Herausforderungen in der Arbeit von Führungskräften. Einer der weltweit renommiertesten Experten auf diesem Gebiet hat basierend auf seinen Erfahrungen aus Forschung und Praxis einen visionären Text geschrieben, der zugleich inspirierend und gefüllt ist mit bedeutenden Implikationen für das Change-Management. Leading Change zeigt Ihnen, wie Sie Wandlungsprozesse in Unternehmen konsequent führen. Beginnend mit den Gründen, warum viele Unternehmen an Change-Prozessen scheitern, wird im Anschluss ein Acht-Stufen-Plan entwickelt, der Ihnen hilft, pragmatisch einen erfolgreichen Wandel zu gestalten. Wenn Sie wissen möchten, warum Ihre letzte Change-Initiative scheiterte, dann lesen Sie dieses Buch am besten gleich, sodass Ihr nächstes Projekt von Erfolg gekrönt wird. Ralf Dobelli, Leading Change is simply the best single work I have seen on strategy implementation. William C. Finnie, Editor-in-Chief Strategy & Leadership Leading Change ist ein weltweiter, zeitloser Bestseller. Werner Seidenschwarz, Seidenschwarz & Comp.

Find eBook