Author	Berndt, Bruce C. author
Title	Ramanujan's Notebooks [electronic resource] : Part III / by Bruce C. Berndt
Imprint	New York, NY : Springer New York : Imprint: Springer, 1991
Connect to	http://dx.doi.org/10.1007/978-1-4612-0965-2
Descript	XIII, 510 p. online resource

During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. Upon Ramanujan's death in 1920, G.H. Hardy strongly urged that Ramanujan's notebooks be published and edited. The English mathematicians G.N. Watson and B.M. Wilson began this task in 1929, but although they devoted nearly ten years to the project, the work was never completed. In 1957, the Tata Institute of Fundamental Research in Bombay published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the tasks of editing Ramanujan's notebooks. Proofs are provided to theorems not yet proven in previous literature, and many results are so startling and different that there are no results akin to them in the literature

16 q-Series and Theta-Functions -- 17 Fundamental Properties of Elliptic Functions -- 18 The Jacobian Elliptic Functions -- 19 Modular Equations of Degrees 3, 5, and 7 and Associated Theta-Function Identities -- 20 Modular Equations of Higher and Composite Degrees -- 21 Eisenstein Series -- References

1. Mathematics
2. Number theory
3. Mathematics
4. Number Theory