By George E. Andrews, Bruce C. Berndt

In the spring of 1976, George Andrews of Pennsylvania nation college visited the library at Trinity university, Cambridge, to envision the papers of the past due G.N. Watson. between those papers, Andrews stumbled on a sheaf of 138 pages within the handwriting of Srinivasa Ramanujan. This manuscript was once quickly unique, "Ramanujan's misplaced notebook." Its discovery has often been deemed the mathematical similar of discovering Beethoven's 10th symphony.

This quantity is the fourth of 5 volumes that the authors plan to put in writing on Ramanujan’s misplaced notebook. not like the 1st 3 books on Ramanujan's misplaced computer, the fourth booklet doesn't specialize in q-series. many of the entries tested during this quantity fall less than the purviews of quantity concept and classical research. numerous incomplete manuscripts of Ramanujan released via Narosa with the misplaced computer are mentioned. 3 of the partial manuscripts are on diophantine approximation, and others are in classical Fourier research and top quantity thought. many of the entries in quantity idea fall less than the umbrella of classical analytic quantity concept. possibly the main interesting entries are hooked up with the classical, unsolved circle and divisor problems.

Review from the second one volume:

"Fans of Ramanujan's arithmetic are guaranteed to be overjoyed through this publication. whereas the various content material is taken at once from released papers, so much chapters comprise new fabric and a few formerly released proofs were more suitable. Many entries are only begging for additional research and may unquestionably 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 activity they're doing. this is often the 1st step...on the best way to an figuring out of the paintings of the genius Ramanujan. it may act as an proposal to destiny generations of mathematicians to take on a role that might by no means be complete."

- Gazette of the Australian Mathematical Society