Ramanujan's Lost Notebook
Part II
(Sprache: Englisch)
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...
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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." The "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work.
Klappentext zu „Ramanujan's Lost Notebook “
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." The "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work.
Inhaltsverzeichnis zu „Ramanujan's Lost Notebook “
Preface.- Introduction.- The Heine Transformation.- The Sears-Thomae Transformation.- Bilateral Series.- Well-poised Series.- Bailey's Lemma and Theta Expansions.- Partial Theta Functions.- Special Identities.- Theta Function Identities.- Ramanujan's Cubic Class Invariant.- Miscellaneous Results on Elliptic Functions and Theta Functions.- Formulas for the Power Series Cofficients of Certain Quotients of Eisenstein Series.- Letters From Matlock House.- Eisenstein Series and Modular Equations.- Series Representable in Terms of Eisenstein Series.- Eisenstein Series and Approximations to p.- Miscellaneous Results on Eisenstein Series.- Location Guide.- Provenance.- References.-
Autoren-Porträt von George E. Andrews, Bruce C. Berndt
In the spring of 1976, George 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. The lost notebook contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work.
Bibliographische Angaben
- Autoren: George E. Andrews , Bruce C. Berndt
- 2010, Softcover reprint of hardcover 1st ed. 2009, XII, 420 Seiten, Masse: 15,6 x 23,7 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1441926666
- ISBN-13: 9781441926661
Sprache:
Englisch
Pressezitat
From the reviews: "This volume contains 16 chapters comprising 314 entries. The material is arranged thematically with the main topics being some of Ramanujan's favorites q series theta functions ... . the authors treatment is extremely thorough. Each chapter contains an introduction with appropriate background. References to all other known proofs of the entries are provided. ... Fans of Ramanujan's mathematics are sure to be delighted by this book. ... Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come." (Jeremy Lovejoy, Mathematical Reviews, Issue 2010 f)
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