Ramanujan's Notebooks: Part III

ISBN-13: 9781461269632 / Angielski / Miękka / 2012 / 510 str.

Bruce C. Berndt; Bruce C. Berndt

Opis

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.

Spis treści

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.

O autorze

During the years 1903-1914, Ramanujan recorded most of his mathematical discoveries without proofs in notebooks. This book is the third of five volumes devoted to the editing of these notebooks. Proofs are provided to theorems not yet proven in the literature, and many results are so startling and different that there are no results akin to them in the literature.