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The Lost Notebook and other unpublished papers. With an introduction by George E. Andrews. (English) Zbl 0639.01023

Berlin: Springer-Verlag; New Delhi: Narosa Publishing House. xxv, 419 pp. (1988).
This volume contains facsimile copies of various manuscripts of S. Ramanujan (1887–1920) along with some correspondence. The first ninety pages reproduce part of the “Lost Notebook”, a collection found in 1965 of more than 600 formulae discovered shortly before Ramanujan’s death. He investigated \(q\)-series, theta functions, continued fractions and partitions. A brief introduction by G. E. Andrews leads the reader into these areas and related published literature.
Letters from Ramanujan to G. H. Hardy with related material from the lost notebook constitute the next section (pages 91–132). A draft paper on properties of \(p(n)\) and \(\tau(n)\) defined by \[ \sum p(n)x^ n=[(1-x)(1- x^ 2)(1-x^ 3)...]^{-1} \] and \[ \sum \tau (n)x^ n=x[(1-x)(1-x^ 2)(1-x^ 3)...]^{24} \] (133–178) is followed by more sheets from the lost notebook (179–215). After a section of pages on several problems (217–243), the volume concludes with a long section entitled other unpublished material including portions of manuscripts (245–419). This is a potpourri of loose pages, sheets from the lost notebook (247–379), correspondence between various mathematicians (380–412), a 1921 letter from E. H. Neville to Nature on Ramanujan’s life and 1923 correspondence from the University of Madras to Hardy on material for a proposed memorial volume.
Since the volume was produced at short notice, there is nothing apart from a brief publisher’s note and Andrew’s introduction (written without exact knowledge of the contents) to guide the reader through the wealth of material nor to explain its choice and arrangement.

MSC:

01A60 History of mathematics in the 20th century
01A75 Collected or selected works; reprintings or translations of classics
11-03 History of number theory
01A70 Biographies, obituaries, personalia, bibliographies

Citations:

Zbl 0138.24201
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