ALMOST A CENTURY OF ANSWERING THE QUESTION: WHAT IS A MOCK THETA FUNCTION?

Quite a few famous and extraordinarily gifted mathematicians led lives that were tragically cut short. Ramanujan is certainly among them. While suffering from a fatal disease, he discovered what he called mock theta functions. Three months before his death in 1920 at the age of 32, he described them in a letter to Hardy that was written under difficultie

Uncovering Ramanujan's "Lost" Notebook: An Oral History

Here we weave together interviews conducted by the author with three prominent figures in the world of Ramanujan's mathematics, George Andrews, Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the "lost" notebook, Andrews and Berndt's effort of proving and editing Ramanujan's notes, and recent breakthroughs by Ono and others carrying certain important aspects of the Indian mathematician's work into the future. Also presented are historical details related to Ramanujan and his mathematics, perspectives on the impact of his work in contemporary mathematics, and a number of interesting personal anecdotes from Andrews, Berndt and Ono

Ramanujan\u27s Master Theorem for Riemannian symmetric spaces

Ramanujan\u27s Master Theorem states that, under suitable conditions, the Mellin transform of a power series provides an interpolation formula for the coefficients of this series. Based on the duality of compact and noncompact reductive Riemannian symmetric spaces inside a common complexification, we prove an analogue of Ramanujan\u27s Master Theorem for the spherical Fourier transform of a spherical Fourier series. This extends the results proven by Bertram for Riemannian symmetric spaces of rank-one. © 2012 Elsevier Inc.