Ramanujan's Lost Notebook

Part I

George E. Andrews, Bruce C. Berndt

438 pages, parution le 03/08/2005

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Résumé

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.

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. Mathematicians are probably several decades away from a complete understanding of those functions. More than half of the material in the book is on q-series, including mock theta functions; the remaining part deals with theta function identities, modular equations, incomplete elliptic integrals of the first kind and other integrals of theta functions, Eisenstein series, particular values of theta functions, the Rogers-Ramanujan continued fraction, other q-continued fractions, other integrals, and parts of Hecke's theory of modular forms.

L'auteur - George E. Andrews

is Evan Pugh Professor of Mathematics at the Pennsylvania State University. He is the author of many books in mathematics, including The Theory o/Partitions (Cambridge University Press). He is a member of the American Academy of Arts and Sciences. In 2003, he was elected to the National Academy of Sciences (USA).

Sommaire

Preface
Introduction
The Rogers-Ramanujan Continued Fraction and Its Modular Properties
Explicit Evaluations of the Rogers-Ramanujan Continued Fraction
A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions
The Rogers-Ramanujan Continued Fraction and Its Connections with Partitions and Lambert Series
Finite Rogers-Ramanujan Continued Fractions
Other q-continued Fractions
Asymptotic Formulas for Continued Fractions
Ramanujan's Continued Fraction for (q2; q3)8/(q; q3)8
The Rogers-Fine Identity
An Empirical Study of the Rogers-Ramanujan Identities
Rogers-Ramanujan-Slater Type Identities
Partial Fractions
Hadamard Products for Two q-Series
Integrals of Theta-functions
Incomplete Elliptic Integrals
Infinite Integrals of q-Products
Modular Equations in Ramanujan's Lost Notebook
Fragments on Lambert Series
Location Guide
Provenance
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	George E. Andrews, Bruce C. Berndt
Parution	03/08/2005
Nb. de pages	438
Format	16 x 24
Couverture	Relié
Poids	756g
Intérieur	Noir et Blanc
EAN13	9780387255293
ISBN13	978-0-387-25529-3