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Introduction

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Abstract

This is the fifth and final volume devoted to an explication of the content of Ramanujan’s Lost Notebook and Other Unpublished Papers [232]. As the title indicates, [232] features the original “Lost Notebook,” discovered by the first author in the library at Trinity College, Cambridge in the spring of 1976. However, [232] also contains several unpublished manuscripts by Ramanujan, letters that Ramanujan wrote to G.H. Hardy from nursing homes, Ramanujan’s last letter to Hardy, and miscellaneous pages by Ramanujan. It has been our goal to cover all of this material.

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References

  1. G.E. Andrews, Mock theta functions in Theta functions–Bowdoin 1987, Part 2, L. Ehrenpreis and R.C. Gunning, eds., Proc. Symp. Pure Math., vol. 49, American Mathematical Society, Providence, RI, 1989, pp. 283–298.

    Google Scholar 

  2. G.E. Andrews and B.C. Berndt, Ramanujan’s Lost Notebook, Part I, Springer, New York, 2005.

    MATH  Google Scholar 

  3. G.E. Andrews and B.C. Berndt, Ramanujan’s Lost Notebook, Part II, Springer, New York, 2009.

    Google Scholar 

  4. G.E. Andrews and B.C. Berndt, Ramanujan’s Lost Notebook, Part III, Springer, New York, 2012.

    Google Scholar 

  5. G.E. Andrews and B.C. Berndt, Ramanujan’s Lost Notebook, Part IV, Springer, New York, 2013.

    Google Scholar 

  6. B.C. Berndt, S.-Y. Kang, and J. Sohn, Finite and infinite Rogers–Ramanujan continued fractions in Ramanujan’s lost notebook, J. Number Thy. 148 (2015), 112–120.

    Article  MathSciNet  Google Scholar 

  7. B.C. Berndt, B. Kim, and K.S. Williams, Euler products in Ramanujan’s lost notebook, Internat. J. Number Thy. 9 (2013), 1313–1349.

    Article  MathSciNet  Google Scholar 

  8. K. Bringmann, A. Folsom, K. Ono, and L. Rolen, Harmonic Maass Forms and Mock Modular Forms: Theory and Applications, Amer. Math. Soc., Providence, 2017.

    Google Scholar 

  9. W. Duke, Almost a century of answering the question: what is a mock theta function?, Not. Amer. Math. Soc. 61 (2014), 1314–1320.

    MathSciNet  MATH  Google Scholar 

  10. A. Folsom, What is …a mock modular form?, Notices Amer. Math. Soc. 57 (2010), 1441–1443.

    MathSciNet  MATH  Google Scholar 

  11. A. Folsom, Perspectives on mock modular forms, J. Number Thy. 176 (2017), 500–540.

    Article  MathSciNet  Google Scholar 

  12. K. Ono, Unearthing the visions of a master: Harmonic Maass forms and number theory, Proc. 2008 Harvard-MIT Current Developments in Mathematics Conference, International Press, Somerville, MA, 2009, pp. 347–454.

    Google Scholar 

  13. K. Ono, The last words of a genius, Notices Amer. Math. Soc. 57 (2010), 1410–1419.

    MathSciNet  MATH  Google Scholar 

  14. S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa, New Delhi, 1988.

    Google Scholar 

  15. L.J. Rogers, Second memoir on the expansion of certain infinite products, Proc. London Math. Soc. 25 (1894), 318–343.

    MathSciNet  Google Scholar 

  16. L.J. Rogers, On two theorems of combinatory analysis and some allied identities, Proc. London Math. Soc. 16 (1917), 315–336.

    Article  Google Scholar 

  17. L.J. Slater, Further identities of the Rogers–Ramanujan type, Proc. London Math. Soc. 54 (1952), 147–167.

    Article  MathSciNet  Google Scholar 

  18. D. Zagier, Ramanujan’s mock theta functions and their applications (after Zwegers and Ono-Bringmann), Astérisque 326 (2009), 143–164.

    MATH  Google Scholar 

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Andrews, G.E., Berndt, B.C. (2018). Introduction. In: Ramanujan's Lost Notebook. Springer, Cham. https://doi.org/10.1007/978-3-319-77834-1_1

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