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: 1435

​​​​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: 9987

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: 8117

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: 2037

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: 4000

Die Lehre von den Kettenbrüchen

Band I: Elementare Kettenbrüche

Author: Oskar Perron

Publisher: Springer-Verlag

ISBN: 3663122891

Category: Mathematics

Page: 194

View: 4276

eigenen Begriffssystemen bereichert worden, die man nicht gerade als jedermann geläufig voraussetzen darf. Die Versuchung lag nahe, durch Heranziehung solcher Theorien den Kettenbrüchen einen gelehrteren Anstrich zu geben. Aber dadurch wäre nicht nur die Lektüre unnötig erschwert, sondern das Wesen der Dinge zumeist verschleiert worden, und es bestände die Gefahr, daß mancher Leser den künstlichen Anstrich für das Wesentliche halten und die harmlose Unschuld, die sich darunter verbirgt, vielleicht gar nicht mehr sehen würde. Deshalb habe ich auf logistische Hieroglyphen, geheimnisvolle "Räume" usw. verzichtet und bin bei der klassischen Wortsprache und den klassischen Rechenmethoden ge blieben. Lediglich zweireihige Matrizes wurden gelegentlich verwandt, nämlich da, wo sie einen wirklichen methodischen Vorteil bieten. Der Matrixkalkül ist ja heute in viel weiteren Kreisen bekannt als vor 40 Jahren und gehört fast schon zu den Elementen; ich habe ihn trotzdem nicht vorausgesetzt, sondern in § 5 das Wenige, was davon gebraucht wird, kurz zusammengestellt. In neuerer Zeit haben die Kettenbrüche auch in der augewandten Mathematik, z. B. in der Elektrotechnik und bei analytischen Approximationsmethoden, Verwendung ge funden. Auch den Vertretern dieser Disziplinen, sowie manchen interessierten Laien, die es trotz unseres materialistischen Zeitalters doch immer noch gibt, glaube ich durch leichte Verständlichkeit besser zu dienen als durch Paradieren mit einer übertriebenen Gelehrsamkeit. Auf die Beigabe einer möglichst lückenlosen Bibliographie habe ich ebenso wie früher verzichtet; man findet eine solche, die von den Anfängen bis ins erste Jahrzehnt unseres Jahrhunderts reicht, bei Wölffing 1.

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 1691

Handbuch der Lehre von der Verteilung der Primzahlen

Author: E. Landau

Publisher: Рипол Классик

ISBN: 5876738352

Category: History

Page: 564

View: 7254

Pi

Algorithmen, Computer, Arithmetik

Author: Jörg Arndt,Christoph Haenel

Publisher: Springer-Verlag

ISBN: 366209360X

Category: Computers

Page: 264

View: 2506

Charlemagne and his heritage

Author: Paul Leo Butzer,Max Kerner,Walter Oberschelp

Publisher: Brepols Publishers

ISBN: N.A

Category: Science

Page: 557

View: 6458

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: 1001

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.

Die Gammafunktion

Author: Niels Nielsen

Publisher: American Mathematical Soc.

ISBN: 9780821838365

Category: Mathematics

Page: 432

View: 2283

This title consists of both original volumes of this classic, now published as one. The first volume is a handbook of the theory of the gamma function. The first part of this volume gives an elementary presentation of the fundamental properties of the gamma function (and related functions) as applications of the theory of analytic functions. The second part covers properties related to the integral representations for $\Gamma(x)$. The third part explores the properties of functions defined via series of factorials: $\Omega(x)=\sum s! a_s/(x(x+1)\ldots(x+s))$, with applications to the gamma function. The Handbook is an often-cited reference in the literature on the gamma function and other transcendental functions. The second (and shorter) volume covers the theory of the logarithmic integral $\mathrm{li}(x)$ and certain related functions. Specific topics include integral representations, asymptotic series, and continued fractions.

Choice

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Academic libraries

Page: N.A

View: 3565

Fünf Minuten Mathematik

100 Beiträge der Mathematik-Kolumne der Zeitung DIE WELT

Author: Ehrhard Behrends

Publisher: Springer-Verlag

ISBN: 3658009985

Category: Mathematics

Page: 262

View: 5231

Das Buch enthält einen Querschnitt durch die moderne und alltägliche Mathematik. Die 100 Beiträge sind aus der Kolumne "Fünf Minuten Mathematik" hervorgegangen, in der verschiedene mathematische Gebiete in einer für Laien verständlichen Sprache behandelt wurden. Der Leser findet hier den mathematischen Hintergrund und viele attraktive Fotos zur Veranschaulichung der Mathematik. Für die Neuauflage wurde der Text aktualisiert und ergänzt; anhand von QR-Codes können zu verschiedenen Themen kurze Filme bei Youtube abgerufen werden.

Krystallsysteme und Krystallstructur

Author: Arthur Schoenflies

Publisher: N.A

ISBN: N.A

Category: Crystallography

Page: 638

View: 8721

Reviews in Number Theory 1973-83

As Printed in Mathematical Reviews

Author: Richard K. Guy

Publisher: American Mathematical Society(RI)

ISBN: N.A

Category: Mathematical reviews

Page: 477

View: 5423

Liebe und Mathematik

Im Herzen einer verborgenen Wirklichkeit

Author: Edward Frenkel

Publisher: Springer-Verlag

ISBN: 3662434210

Category: Mathematics

Page: 317

View: 541

Opera minora

Author: Ulrich Schneider,Marion Meisig

Publisher: Otto Harrassowitz Verlag

ISBN: 9783447047005

Category: History

Page: 273

View: 430

In das Jahr 2002 fallt sowohl der achtzigste Geburtstag Ulrich Schneiders als auch sein zehnter Todestag, ein Anlass, die Opera minora dieses bedeutenden Indologen in einem Band gesammelt und neu gesetzt erscheinen zu lassen. Die Aufsatze geben einen reprasentativen Querschnitt durch das wissenschaftliche Werk Ulrich Schneiders und zeichnen dessen Entwicklung nach. Die Abhandlungen demonstrieren Schneiders umfassendes Fachverstandnis; sie dokumentieren seine Forschungen zum indischen Kulturkreis unter Einbeziehung der Fachrichtungen Philologie, Philosophie, Religionsgeschichte, Literaturwissenschaft, Sprachwissenschaft, Epigraphik und Ikonographie.

Der geniale Mensch

Author: Cesare Lombroso

Publisher: N.A

ISBN: N.A

Category: Genius

Page: 447

View: 964

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