AMS Chelsea Publishing 1927; 426 pp; hardcover Volume: 159 Reprint/Revision History: first AMS printing 2000 ISBN10: 0821820761 ISBN13: 9780821820766 List Price: US$58 Member Price: US$52.20 Order Code: CHEL/159.H
 The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems, and letters have spawned a remarkable number of later results by many different mathematicians. Here, his 37 published papers, most of his first two and last letters to Hardy, the famous 58 problems submitted to the Journal of the Indian Mathematical Society, and the commentary of the original editors (Hardy, Seshu Aiyar and Wilson) are reprinted again, after having been unavailable for some time. In this printing of Ramanujan's collected papers, Bruce Berndt provides an annotated guide to Ramanujan's work and to the mathematics it inspired over the last threequarters of a century. The historical development of ideas is traced in the commentary and by citations to the copious references. The editor has done the mathematical world a tremendous service that few others would be qualified to do. Readership Graduate students and research mathematicians interested in number theory. Table of Contents  Some properties of Bernoulli's numbers
 On Question 330 of Prof. Sanjana
 Note on a set of simultaneous equations
 Irregular numbers
 Squaring the circle
 Modular equations and approximations to \(\pi\)
 On the integral \(\int^x_0\frac{\tan^{1}t}{t}dt\)
 On the number of divisors of a number
 On the sum of the square roots of the first \(n\) natural numbers
 On the product \(\prod^{n=\infty}_{n=0}[1+(\frac{x}{a+nd})^3]\)
 Some definite integrals
 Some definite integrals connected with Gauss's sums
 Summation of a certain series
 New expressions for Riemann's functions \(\xi(s)\) and \(\Xi(t)\)
 Highly composite numbers
 On certain infinite series
 Some formulæ in the analytic theory of numbers
 On certain arithmetical functions
 A series for Euler's constant \(\gamma\)
 On the expression of a number in the form \(ax^2 + by^2 + cz^2 +du^2\)
 On certain trigonometrical sums and their applications in the theory of numbers
 Some definite integrals
 Some definite integrals
 A proof of Bertrand's postulate
 Some properties of \(p(n)\), the number of partitions of \(n\)
 Proof of certain identities in combinatory analysis
 A class of definite integrals
 Congruence properties of partitions
 Algebraic relations between certain infinite products
 Congruence properties of partitions
 Une formule asymptotique pour le nombre des partitions de \(n\)
 Proof that almost all numbers \(n\) are composed of about \(\log \log n\) prime factors
 Asymptotic formulæ in combinatory analysis
 Asymptotic formulæ for the distribution of integers of various types
 The normal number of prime factors of a number \(n\)
 Asymptotic formulæ in combinatory analysis
 On the coefficients in the expansions of certain modular functions
 Questions and solutions
 Appendix I: Notes on the papers
 Appendix II: Further extracts from Ramanujan's letters to G. H. Hardy
 Commentary on Ramanujan's collected papers
