Collected papers of Srinivasa Ramanujan. Edited by G. H. Hardy, P. V. Seshu Aiyar, B. M. Wilson. (Q1444365)

Die gesammelten Werke enthalten die folgenden Abhandlungen: \{The web source provides links to all full-texts!\}. 1. Some properties of Bernoulli's numbers (1911) [J. Indian Math. Soc. 3, 219--234 (1911; JFM 42.0460.02)]. 2. On Question 330 of Prof. Sanjana (1912) [J. Indian Math. Soc. 4, 59--61 (1912; JFM 43.0343.03)]. 3. Note on a set of simultaneous equations (1912) [J. Indian Math. Soc. 4, 94--96 (1912; JFM 43.0157.01)]. 4. Irregular numbers (1913) [J. Indian Math. Soc. 5, 105--106 (1913; JFM 44.0213.03)]. 5. Squaring the circle (1913) [J. Indian Math. Soc. 5, 132 (1913; JFM 44.0583.03)]. 6. Modular equations and approximations to \(\pi\) (1914) [Q. J. Math. 45, 350--372 (1914; JFM 45.1249.01)]. 7. On the integral \({\displaystyle\int\limits_0^\pi} \dfrac{\tan^{-1}t}t\,dt\) (1915) [J. Indian Math. Soc. 7, 93--96 (1915)]. 8. On the number of divisors of a number (1915) [J. Indian Math. Soc. 7, 131--133 (1915)]. 9. On the sum of the square roots of the first \(n\) natural numbers (1915) [Journal of the Indian Mathematical Society 7, 173--175 (1915)]. 10. On the product \(\prod\limits_{n=0}^{n=\infty} \left[1+\left(\dfrac x{a+nd}\right)^3\right]\) (1915) [J. Indian Math. Soc. 7, 209--211 (1915)]. 11. Some definite integrals (1915) [Messenger Math. 44, 10--18 (1915; JFM 45.0464.03)]. 12. Some definite integrals connected with Gauss's sums (1915) [Messenger Math. 44, 75--85 (1915; JFM 45.0460.02)]. 13. Summation of certain series (1915) [Messenger Math. 44, 157--160 (1915; JFM 45.1277.02)]. 14. New expressions for Riemann's functions \(\xi(s)\) and \(\varXi(t)\) (1915) [Q. J. Math. 46, 253--260 (1915; JFM 45.1343.05)]. 15. Highly composite numbers (1915) [Proc. Lond. Math. Soc. (2) 14, 347--409 (1916; JFM 45.1248.01)]. 16. On certain infinite series (1916) [Messenger Math. 46, 11--16 (1916; JFM 45.1277.01)]. 17. Some formulae in the analytic theory of numbers (1916) [Messenger Math. 46, 81-84 (1916)]. 18. On certain arithmetical functions (1916). [Trans. Camb. Philos. Soc. 22, 159--184 (1916; Zbl 07426016)]. 19. A series for Euler's constant \(\gamma\) (1917). 20. On the expressions of a number in the form \(ax^2 + by^2 + cz^2 + du^2\) (1917). 21. On certain trigonometrical sums and their applications in the theory of numbers (1918) [Trans. Camb. Philos. Soc. 22, No. 13, 259--276 (1918)]. 22. Some definite integrals (1918). 23. Some definite integrals (1919). 24. A proof of Bertrand's postulate (1919). 25. Some properties of \(p(n)\), the number of partitions of \(n\) (1919). 26. Proof of certain identities in combinatory analysis (1919). 27. A class of definite integrals (1920). 28. Congruence properties of partitions (1920; JFM 48.0150.02). 29. Algebraic relations between certain infinite products (1920; JFM 47.0904.05). 30. Congruence properties of partitions (1921). Ferner die folgenden gemeinsam mit G. H. Hardy geschriebenen Arbeiten: 31. Une formule asymptotique pour le nombre des partitions de \(n\) (1917). 32. Proof that almost all numbers \(n\) are composed of about \(\log \log n\) prime factors (1917). 33. Asymptotic formulae in combinatory analysis (1917). 34. Asymptotic formulae for the distribution of integers of various types (1917). 35. The normal number of prime factors of a number \(n\) (1917). [Q. J. Math. 48, 76--92 (1917; JFM 46.0262.03). 36. Asymptotic formulae in combinatory analysis (1918). 37. On the coefficients in the expansions of certain modular functions (1918). Dem Werk sind ferner alle von Ramanujan im J. Indian Math. Soc. gestellten Aufgaben und die von Ramanujan veröffentlichten Lösungen beigegeben. Ein Anhang bringt Bemerkungen der Herausgeber zu den Arbeiten, sowie Auszüge aus dem Briefwechsel mit G. H. Hardy. Das Buch enthält als Einleitung eine von \textit{P. V. Seshu Aiyar} und \textit{R. Ramachandra Rao} geschriebene ausführliche Biographie, sowie einen Wiederabdruck des von \textit{G. H. Hardy} gehaltenen Nachrufes [Proc. Lond. Math. Soc. (2) 19, XL--XLVIII (1921; JFM 48.0019.04)]. (Updated 2011).