Preface
Generally acknowledged as India's greatest mathematician, Srinivasa
Ramanujan is most often thought of as a number theorist, although
he made substantial contributions to analysis and several other ar-
eas of mathematics. For most number theorists, when Ramanujan's
name is mentioned, the partition and tau functions immediately come
to mind. His interest in these arithmetic functions was inextricably
intertwined with his primary interests of theta functions and other q-
series. In fact, most of Ramanujan's research in number theory arose
out of g-series and theta functions. Theta functions are the fundamen-
tal building blocks in the theory of elliptic functions, and Ramanujan
independently developed his own theory of elliptic functions, which is
quite unlike the classical theory. We do not formally define an elliptic
function, but, roughly, elliptic functions are meromorphic functions
with two linearly independent periods over the real numbers. The
concept of double periodicity is not used in this book, and, to the
best of our knowledge, Ramanujan never utilized this idea.
The purpose of this book is to provide an introduction to this
large expanse of Ramanujan's work in number theory. Needless to
say, we shall be able to cover only a very small fraction of Ramanu-
jan's work on theta functions and g-series and their connections with
number theory. However, after developing only a few facts about
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