Bruce BerndtAffiliation: University of Illinois Email: berndt@math.uiuc.edu Title Of Talk 1: The Circle Problem, The Divisor Problem, and Two Bessel Series Expansions in Ramanujan's Lost Notebook Abstract: On page 335 in the volume containing his Lost Notebook, Ramanujan recorded two identities, each involving a double series of Bessel functions. One of the identities has been proved (in a sense), while the other is close to being proved (in a sense). One is connected with the famous circle problem, while the other is connected with the equally famous divisor problem. We review these impenatrable, unsolved problems, discuss what we know about them, and show their connections with Ramanujan's two formulas. A discussions of proofs and attempted proofs of Ramanujan's formulas will be a focus of our expository talk. Title Of Talk 2: Questions about Four Sets of Problems from Ramanujan's Lost Notebook
Last update made Thu Mar 18 12:56:34 EDT 2010.
|