The Lost Notebook and Other Unpublished Papers

"The Lost Notebook", with an introduction by George E. Andrews and a short biography by S. Raghavan, consists of 90 unpaginated sheets representing Ramanujan's work on q-series and other topics followed by letters written by Ramanujan to G.H. Hardy on many mathematical topics including "coefficients in the 1 / g3 and 1g2 problems" as well as the only available remnant of his famous letter dated 12th January 1920 on mock theta functions. The nearly 650 formulas in "The Lost Notebook" cover approximately: q-series and related topics including mock functions, 60 per cent Modular equations and relations, singular moduli, 30 per cent Integrals, Dirichlet series, congruences, asymptotics, miscellaneous, 10 per cent "The Lost Notebook" includes a hitherto unpublished manuscript of Ramanujan's on "Properties of p(n) and (n)," dealing with congruence relation satisfied by these arithmetical functions, 28 sheets copied from the "Loose Papers" of Ramanujan held in the Trinity College Library which include notes on "Reciprocal functions", "Approximate summation of series involving prime numbers", Ramanujan's discoveries on Euler products for Dirichlet series associated to modular forms and Ramanujan's "forty identities", with relevant sheets in Ramanujan's handwriting. The subsequent 117 pages include Ramanujan's unpublished work related to "Highly composite numbers" and "On certain trignometrical sums - " with Hardy's notings thereon as also class invariants listed by Ramanujan with a host of interesting identities of an arithmetic nature. "The Lost Notebook" also carries letters between J.E. Littlewood, G.H. Hardy, Ramanujan and G.N. Watson, etc. with a bearing on Ramanujan's work and various other letters of some significance including E.H. Neville's letter on Ramanujan extracted from Nature of 20th January 1921.