Collected Papers of Srinivasa Ramanujan

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 π; 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.