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Ramanujan's Lost Notebook - Part IV (Paperback, 2013 ed.)
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Ramanujan's Lost Notebook - Part IV (Paperback, 2013 ed.)
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In the spring of 1976, George Andrews of Pennsylvania State
University visited the library at Trinity College, Cambridge, to
examine the papers of the late G.N. Watson. Among these papers,
Andrews discovered a sheaf of 138 pages in the handwriting of
Srinivasa Ramanujan. This manuscript was soon designated,
"Ramanujan's lost notebook." Its discovery has frequently been
deemed the mathematical equivalent of finding Beethoven's tenth
symphony. This volume is the fourth of five volumes that the
authors plan to write on Ramanujan's lost notebook. In contrast to
the first three books on Ramanujan's Lost Notebook, the fourth book
does not focus on q-series. Most of the entries examined in this
volume fall under the purviews of number theory and classical
analysis. Several incomplete manuscripts of Ramanujan published by
Narosa with the lost notebook are discussed. Three of the partial
manuscripts are on diophantine approximation, and others are in
classical Fourier analysis and prime number theory. Most of the
entries in number theory fall under the umbrella of classical
analytic number theory. Perhaps the most intriguing entries are
connected with the classical, unsolved circle and divisor problems.
Review from the second volume: "Fans of Ramanujan's mathematics are
sure to be delighted by this book. While some of the content is
taken directly from published papers, most chapters contain new
material and some previously published proofs have been improved.
Many entries are just begging for further study and will
undoubtedly be inspiring research for decades to come. The next
installment in this series is eagerly awaited." - MathSciNet Review
from the first volume: "Andrews and Berndt are to be congratulated
on the job they are doing. This is the first step...on the way to
an understanding of the work of the genius Ramanujan. It should act
as an inspiration to future generations of mathematicians to tackle
a job that will never be complete." - Gazette of the Australian
Mathematical Society
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