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First
page of 'Lost' Notebook
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The 'Lost' notebook of Ramanujan, discovered by Prof. George E.
Andrews, in the spring of 1976, had been earlier 'found' in November
1965 by Dr. J.M. Whittaker lying loose on the floor among Watson's
papers. These papers were obviously part of papers dispatched
from India to Hardy, in August 1923, a few years after the death
of Ramanujan. It is not clear after all these years whether these
were scrutinized or not by Watson and Wilson who took up the task
of editing the notebooks at the instance of Hardy. However, Prof.
Robert A. Rankin has classified all the papers which are now in
the Wren library and this work of classifying was done in the
year 1968. Today, these papers are found in one of three large
card board boxes (each foolscap size box is about 2 inches thick)
in the archives of the Wren library. One of the items (subsequently
catalogued and) accessible with Add.Ms.a.94 is:S.Ramanujan: "Lost
Notebook" on q-series and similar types, n.d.In the appendices
at the end of this book the reader will find all the papers of
Ramanujan with the Wren library, the National Archives in New
Delhi and the Tamil Nadu Archives in Chennai.Srinivasa Ramanujan
- The Lost Notebook and Other Unpublished Papers, has an introduction
by George E. Andrews. The following Publisher's Note is self-explanatory
as regards the contents of this book:In this collection of unpublished
manuscripts of Srinivasa Ramanujan, we have first reproduced a
major portion of the "Lost Notebook", consisting of
90 unpaginated sheets representing his work on q-series and other
topics. The "Lost Notebook" was brought to light in
the spring of 1976 as "part of the Watson bequest" by
Professor G.E. Andrews whose introduction precedes the text of
the "Lost Notebook" reproduced here. This is followed
by letters written by Ramanujan to G.H. Hardy during his stay
in English nursing homes, on many mathematical topics including
"coeffcients in the 1/g3, and 1/g2 problems" as well
as the only available remnant of his famous letter dated 12 January
1920 on mock theta functions. Various sheets in Ramanujan's handwriting
seemingly related to these letters have been inserted close to
them. Next, we have provided a hitherto unpublished manuscript
of Ramanujan's on "Properties of p(n) and t(n) …"
dealing with congruence relations satisfied by these arithmetic
functions. One may find, thereafter, 28 sheets copied from the
"Loose Papers" of Ramanujan held in the Trinity College
Library; these include a note on "Reciprocal functions",
another concerning "Approximate summation of series involving
prime numbers", Ramanujan's marvelous discoveries on Euler
products of Dirichlet series associated to modular forms and his
famous "forty identities", with relevant sheets in Ramanujan's
handwriting juxtaposed. …The subsequent 117 pages include
Ramanujan's unpublished work related to various papers of his,
especially in continuation of the one entitled "Highly composite
numbers" and "On certain trigonometrical sums …
with Hardy's noting there on; besides, one may find here class
invariants listed by Ramanujan and a host of interesting identities
of an arithmetic nature.At the end, we have taken care not to
miss out on interesting letters from J.E. Littlewood to G.H. Hardy,
G.H. Hardy to Ramanujan, G.H. Hardy to G.N. Watson, etc. with
a bearing on Ramanujan's work and various other letters of significance.
Fragments in Ramanujan's handwriting have all been arranged as
appropriately as possible. This last section contains also E.H.
Neville's letter on Ramanujan extracted from Nature of 20 January
1921. From the above Publisher's Note it is clear that the volume
brought out on the occasion of the Ramanujan birth centenary as
a companion volume to the two volume facsimile edition of Ramanujan's
notebooks contains a lot more information which would be of interest
to the mathematicians. Narosa Publishing House has thus the set
of three volumes on the notebooks of Ramanujan which is a must
for any good mathematics library anywhere in the world.
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