Collected Papers of Srinivasa Ramanujan

Originally published in 1927, this book presents the collected papers of the renowned Indian mathematician Srinivasa Ramanujan (1887–1920).

Srinivasa Ramanujan (Author), G. H. Hardy (Edited by), P. V. Seshu Aiyar (Edited by), B. M. Wilson (Edited by)

9781107536517, Cambridge University Press

Paperback / softback, published 3 December 2015

392 pages
25.4 x 17.9 x 2 cm, 0.77 kg

'[The book] is introduced by a pair of notes which are sources of wonderful information about Ramanujan in their own right, both as regards his life and his mathematics. After that it is all about his mathematics: thirty-seven articles on number theory, infinite series, integrals, and combinatorics. It is all stunning, both by virtue of the content of these articles and because of the idiosyncrasy of their author.' Michael Berg, MAA Reviews

Originally published in 1927, this book presents the collected papers of the renowned Indian mathematician Srinivasa Ramanujan (1887–1920), with editorial contributions from G. H. Hardy (1877–1947). Detailed notes are incorporated throughout and appendices are also included. This book will be of value to anyone with an interest in the works of Ramanujan and the history of mathematics.

Preface
Notice P. V. Seshu and R. Bamachaundra Rao
Notice G. H. Hardy
Part I. Papers: 1. Some properties of Bernoulli's numbers
2. On question 330 of Prof. Sanjana
3. Note on a set of simultaneous equations
4. Irregular numbers
5. Squaring the circle
6. Modular equations and approximations to ?
7. On the integral [...]
8. On the number of divisors of a number
9. On the sum of the square roots of the first n natural numbers
10. On the product [...]
11. Some definite integrals
12. Some definite integrals connected with Gauss's sums
13. Summation of a certain series
14. New expression for Riemann's functions [...]
15. Highly composite numbers
16. On certain infinite series
17. Some formulae in the analytic theory of numbers
18. On certain arithmetical functions
19. A series of Euler's constant y
20. On the expression of a number in the form of ax2+by2+cz2+du2
21. On certain trigonometrical sums and their applications in the theory of numbers
22. Some definite integrals
23. Some definite integrals
24. A proof of Bertrand's postulate
25. Some properties of p (n), the number of partitions of n
26. Proof of certain identities in combinatory analysis
27. A class of definite integrals
28. Congruence properties of partitions
29. Algebraic relations between certain infinite products
30. Congruence properties of partitions
29. Algebraic relations between certain infinite products
30. Congruence properties of partitions
Part II. Papers Written in Collaboration with G. H. Hardy: 31. Une formule asymptotique pour le nombre des partitions de n
32. Proof that almost all numbers n are composed of about log log n prime factors
33. Asymptotic formulae in combinatory analysis
34. Asymptotic formulae for the distribution of integers of various types
35. The normal number of prime factors of a number n
36. Asymptotic formulae in combinatory analysis
37. On the coefficients in the expansions of certain modular functions
Questions and solutions
Appendix 1. Notes on the papers
Appendix 2. Further extracts from Ramanujan's letters to G. H. Hardy.

Subject Areas: History of mathematics [PBX]