Ramanujan's Lost Notebook


Author: George E. Andrews,Bruce C. Berndt
Publisher: Springer Science & Business Media
ISBN: 1461440815
Category: Mathematics
Page: 439
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​​​​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​

Surveys in Number Theory


Author: Krishnaswami Alladi
Publisher: Springer Science & Business Media
ISBN: 0387785108
Category: Mathematics
Page: 188
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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
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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: 1836

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Ramanujan’s Notebooks


Author: Bruce C. Berndt
Publisher: Springer Science & Business Media
ISBN: 1461216249
Category: Mathematics
Page: 624
View: 5477

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The fifth and final volume to establish the results claimed by the great Indian mathematician Srinivasa Ramanujan in his "Notebooks" first published in 1957. Although each of the five volumes contains many deep results, the average depth in this volume is possibly greater than in the first four. There are several results on continued fractions - a subject that Ramanujan loved very much. It is the authors wish that this and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujans remarkable ideas.

Meine Zahlen, meine Freunde

Glanzlichter der Zahlentheorie
Author: Paulo Ribenboim
Publisher: Springer-Verlag
ISBN: 3540879579
Category: Mathematics
Page: 391
View: 9341

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Paulo Ribenboim behandelt Zahlen in dieser außergewöhnlichen Sammlung von Übersichtsartikeln wie seine persönlichen Freunde. In leichter und allgemein zugänglicher Sprache berichtet er über Primzahlen, Fibonacci-Zahlen (und das Nordpolarmeer!), die klassischen Arbeiten von Gauß über binäre quadratische Formen, Eulers berühmtes primzahlerzeugendes Polynom, irrationale und transzendente Zahlen. Nach dem großen Erfolg von „Die Welt der Primzahlen" ist dies das zweite Buch von Paulo Ribenboim, das in deutscher Sprache erscheint.

Pi

Algorithmen, Computer, Arithmetik
Author: Jörg Arndt,Christoph Haenel
Publisher: Springer-Verlag
ISBN: 366209360X
Category: Computers
Page: 264
View: 1724

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Eine kleine Geschichte der Unendlichkeit


Author: Brian Clegg
Publisher: Rowohlt Verlag GmbH
ISBN: 364404371X
Category: Fiction
Page: 352
View: 4476

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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
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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.

Liebe und Mathematik

Im Herzen einer verborgenen Wirklichkeit
Author: Edward Frenkel
Publisher: Springer-Verlag
ISBN: 3662434210
Category: Mathematics
Page: 317
View: 7415

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Choice


Author: N.A
Publisher: N.A
ISBN: N.A
Category: Academic libraries
Page: N.A
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Begriffs- und Wortbedeutungsentwicklung

Theoretische, empirische und methodische Untersuchungen
Author: Thomas B. Seiler,Wolfgang Wannenmacher
Publisher: Springer-Verlag
ISBN: 3642704891
Category: Psychology
Page: 292
View: 9303

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Untersuchungen über höhere Arithmetik


Author: Carl Friedrich Gauss
Publisher: American Mathematical Soc.
ISBN: 0821842137
Category: Mathematics
Page: 695
View: 974

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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).

Fünf Minuten Mathematik

100 Beiträge der Mathematik-Kolumne der Zeitung Die Welt
Author: Ehrhard Behrends
Publisher: Springer-Verlag
ISBN: 9783834800824
Category:
Page: 256
View: 8064

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Feynmans Regenbogen

die Suche nach Schönheit in der Physik und im Leben
Author: Leonard Mlodinow
Publisher: N.A
ISBN: 9783379008266
Category:
Page: 204
View: 5612

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