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A look back at Ramanujan's Notebooks

Published online by Cambridge University Press:  24 October 2008

B. J. Birch
B. J. Birch
Affiliation:
Brasenose College, Oxford
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Extract

Ramanujan's notebooks were the theme of a lecture (20) given by G. N. Watson to the London Mathematical Society in 1931. At that time, he and B. M. Wilson were collaborating on a critical edition; Watson was anticipating that the task might take a further 5 years. Unhappily, Wilson died, and the task of editing the notebooks has never been completed.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 1 , July 1975 , pp. 73 - 79
Copyright
Copyright © Cambridge Philosophical Society 1975

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References

REFERENCES

(1)Atkin, A. O. L. Congruences for modular forms, in Computers in mathematical research, (Churchhouse, R. F. and Herz, J.-C. editors) pp. 8–19. (North Holland, Amsterdam, 1968.)Google Scholar
(2)Darling, H. B. C.Proofs of certain identities and congruences enunciated by S. Ramanujan, Proc. London Math. Soc. (2) 19 (1921), 350–372.CrossRefGoogle Scholar
(3)Hardy, G. H.Ramanujan (Cambridge, 1940).Google Scholar
(4)Hecke, E.Neuere Fortschritte in der Theorie der elliptischen Modulfunktionen. Comptes rendus du Congrès international des Mathematiciens, Oslo 1936, pp. 140–156.Google Scholar
(5)Hecke, E.Über Modulfunktionen und die Dirichletschen Reihen mit Eulerscher Produktentwicklung. I. Math. Ann. 114 (1937), 1–28.CrossRefGoogle Scholar
(6)Mordell, L. J.On Mr Ramanujan's empirical expansions of modular functions. Proc. Cambridge Philos. Soc. 19 (1917), 117–124.Google Scholar
(7)Mordell, L. J.Note on certain modular relations considered by Messrs Ramanujan, Darling and Rogers. Proc. London Math. Soc. (2), 20 (1922), 408–416.CrossRefGoogle Scholar
(8)Ogg, A.Modular forms and Dirichlet series (Benjamin, New York, 1969.)Google Scholar
(9)Ramanujan, S.Collected Papers (Cambridge, 1927).Google Scholar
(10)Ramanujan, S.Notebooks of Srinivasa Ramanujan (Tata Institute for Fundamental Research, Bombay, 1957).Google Scholar
(11)Ramanujan, S.Highly composite numbers. Proc. London Math. Soc. (2), 14 (1915), 347–409.CrossRefGoogle Scholar
(12)Ramanujan, S.On certain arithmetical functions. Trans. Cambridge Philos. Soc. 22, No. 9 (1916), 159–184.Google Scholar
(13)Ramanujan, S.A proof of Bertrand's postulate. J. Indian Math. Soc. 11 (1919), 181–182.Google Scholar
(14)Ramanujan, S.Some properties of p(n), the number of partitions of n. Proc. Cambridge Philos. Soc. 19 (1919), 207–210.Google Scholar
(15)Ramanujan, S.Algebraic relations between certain infinite products. Proc. London Math. Soc. (2), 18 (1920), xx.Google Scholar
(16)Ramanujan, S.Congruence properties of partitions. Math. Z. 9 (1921), 147–153.CrossRefGoogle Scholar
(17)Rogers, L. J.On a type of modular relation. Proc. London Math. Soc. (2), 19 (1921), 387–397.CrossRefGoogle Scholar
(18)Serre, J.-P. Formes modulaires et fonctions zĕta p-adiques, in Modular Functions of One Variable III, 191–268. Lecture Notes in Mathematics 350 (Springer-Verlag Heidelberg, 1973).Google Scholar
(19)Swinnerton-Dyer, H. P. F. On 1-adic representations and congruences for coefficients of modular forms, in Modular functions of one variable III, 1–55. Lecture Notes in Mathematics 350 (Springer-Verlag Heidelberg, 1973).Google Scholar
(20)Watson, G. N.Ramanujan's note books. J. London Math. Soc. 6 (1931), 137–153.CrossRefGoogle Scholar
(21)Watson, G. N.Proof of certain identities in combinatory analysis. J. Indian Math. Soc. 20 (1933), 57–69.Google Scholar
(22)Watson, G. N.Über Ramanujansche Kongruenzeigenschaften der Zerfällungsanzahlen. Math.Z. 39 (1935), 712–731.CrossRefGoogle Scholar
(23)Watson, G. N.Ramanujans Vermutung über Zerfällungsanzahlen. J. Zeine Angew. Math. 179 (1938), 97–128.CrossRefGoogle Scholar