By George E. Andrews, Bruce C. Berndt

In the spring of 1976, George Andrews of Pennsylvania country collage visited the library at Trinity university, Cambridge, to check the papers of the past due G.N. Watson. between those papers, Andrews came upon a sheaf of 138 pages within the handwriting of Srinivasa Ramanujan. This manuscript used to be quickly distinct, "Ramanujan's misplaced notebook." Its discovery has usually been deemed the mathematical an identical of discovering Beethoven's 10th symphony.

This quantity is the fourth of 5 volumes that the authors plan to write down on Ramanujan’s misplaced notebook. not like the 1st 3 books on Ramanujan's misplaced laptop, the fourth booklet doesn't concentrate on q-series. many of the entries tested during this quantity fall below the purviews of quantity concept and classical research. a number of incomplete manuscripts of Ramanujan released by way of Narosa with the misplaced pc are mentioned. 3 of the partial manuscripts are on diophantine approximation, and others are in classical Fourier research and major quantity concept. many of the entries in quantity concept fall below the umbrella of classical analytic quantity conception. possibly the main fascinating entries are attached with the classical, unsolved circle and divisor problems.

Review from the second one volume:

"Fans of Ramanujan's arithmetic are absolute to be thrilled by means of this ebook. whereas a number of the content material is taken at once from released papers, so much chapters comprise new fabric and a few formerly released proofs were stronger. Many entries are only begging for additional learn and should surely be inspiring learn for many years to come back. the subsequent installment during this sequence is eagerly awaited."

- MathSciNet

Review from the 1st volume:

"Andrews and Berndt are to be congratulated at the task they're doing. this is often the 1st step...on the right way to an realizing of the paintings of the genius Ramanujan. it's going to act as an notion to destiny generations of mathematicians to take on a role that would by no means be complete."

- Gazette of the Australian Mathematical Society