Ramanujan's lost notebook

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Srinivasa Ramanujan's lost notebook is the manuscript in which Ramanujan, the great Indian mathematician and later a Fellow of Trinity College, Cambridge, recorded the mathematical discoveries of the last year of his life. It was rediscovered by George Andrews in 1976, in a box of effects of G. N. Watson stored at the Wren Library at Trinity College, Cambridge. The "notebook" is not a book, but consists of 87 loose and unordered sheets of paper, with more than 600 of Ramanujan's formulas.

George E. Andrews and Bruce C. Berndt (2005, 2009) have published several books in which they give proofs for Ramanujan's formulas included in the notebook. Berndt says of the notebooks' discovery: "The discovery of this 'Lost Notebook' caused roughly as much stir in the mathematical world as the discovery of Beethoven’s tenth symphony would cause in the musical world." (Peterson 2006)

History

After Ramanujan died on April 26, 1920, at the age of 32, his wife gave his notebooks to the University of Madras. On August 30, 1923, the registrar Francis Drewsbury sent much of this material to G. H. Hardy, probably including the lost notebook. Some time between 1934 and 1947 Hardy passed the notebook on to G. N. Watson. After Watson's death in 1965, J. M. Whittaker examined Watson's papers (which were a complete mess, due to be incinerated in a few days) and found Ramanujan's notebook, which he and R. A. Rankin sent to Trinity College library on December 26, 1968. George Andrews (1985, section 1.5) found the lost notebook in the spring of 1976 while on a visit to Trinity College, and it was published on December 22, 1987 by Narosa publishing house.

Contents of the notebook

Rankin (1989) described the lost notebook in detail. The majority of the formulas are about q-series and mock theta functions, about a third are about modular equations and singular moduli, and the remaining formulas are mainly about integrals, Dirichlet series, congruences, and asymptotics.

References

  • Berndt, Bruce C.; Evans, Ronald J. (1983), "Chapter 7 of Ramanujan's second notebook", Proc. Indian Acad. Sci. (Math. Sci.), 92 (2): 67–96, doi:10.1007/BF02863011, MR 0755124.
  • Berndt, Bruce C. (1983), "Chapter 11 of Ramanujan's second notebook", Bull. London Math. Soc., 15 (4): 273–320, doi:10.1112/blms/15.4.273, MR 0703753.
  • Alladi, Krishnaswami (Feb 17, 2005), "Ramanujan's lost notebook: a lecture series in Florida", The Hindu
  • Andrews, George E. (1986), q-series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra, CBMS Regional Conference Series in Mathematics, 66, Published for the Conference Board of the Mathematical Sciences, Washington, DC, ISBN 978-0-8218-0716-3, MR 0858826
  • Andrews, George E.; Berndt, Bruce C. (2005), Ramanujan's lost notebook. Part I, Berlin, New York: Springer-Verlag, ISBN 978-0-387-25529-3, MR 2135178, OCLC 228396300
  • Andrews, George E.; Berndt, Bruce C. (2009), Ramanujan's lost notebook. Part II, Berlin, New York: Springer-Verlag, ISBN 978-0-387-77765-8, MR 2474043
  • Andrews, George E.; Berndt, Bruce C. (2012), Ramanujan's lost notebook. Part III, Berlin, New York: Springer-Verlag, ISBN 978-1-4614-3809-0
  • Askey, Richard (1988), "Book Review: The lost notebook and other unpublished papers", American Mathematical Society. Bulletin. New Series, 19 (2): 558–560, doi:10.1090/S0273-0979-1988-15741-2, ISSN 0002-9904, MR 1567721
  • Peterson, Doug (2006), "Raiders of the Lost Notebook", LASNews, retrieved 2009-02-19
  • Ramanujan, Srinivasa (1988), The lost notebook and other unpublished papers, New Delhi; Berlin, New York: Narosa Publishing House; Springer-Verlag, ISBN 978-3-540-18726-4, MR 0947735 Reprinted 2008 ISBN 978-81-7319-947-9
  • Rankin, Robert A. (1989), "Ramanujan's manuscripts and notebooks. II", Bull. London Math. Soc., 21 (4): 351–365, doi:10.1112/blms/21.4.351, ISSN 0024-6093, MR 0998632

External links