Book Review: The lost notebook and other unpublished papers

Abstract

The so-called Lost Notebook of S.R. Ramanujan was brought to light in 1976 as part of the Watson bequest, by G.E. Andrews with whose introduction this collection of unpublished manuscripts opens. A major portion of the Lost Notebook - really just 90 unpaginated sheets of work on q-series and other topics - is reproduced here in facsimile. Letters from Ramanujan to Hardy as well as various other sheets of seemingly related notes are then included, on topics including coefficients in the 1/q3 and 1/q2 problems and the mock theta functions. The next 180 pages consist of unpublished manuscripts of Ramanujan, including 28 pages from the 'Loose Papers` held in the Trinity College Library. Finally a number of interesting letters that were exchanged between Ramanujan, Littlewood, Hardy and Watson, with a bearing on Ramanujan's work are collected together here with other extracts and fragments. The lost notebook -- Letters from Srinivasa Ramanujan to G.H. Hardy and some sheets from the lost notebook -- Properties of p(n) and τ(n) -- Loose papers on reciprocal functions, approximate summations of series involving prime numbers, Euler products for Dirichlet series and Forty identities, etc. -- Other unpublished papers.