Two identities in Ramanujan’s Lost Notebook with Bessel function series

Sun Kim (김선)

Mathematical Institute, University of Cologne, Cologne, Germany

Mathematical Institute, University of Cologne, Cologne, Germany

2019/11/05 Tue 4:30PM-5:30PM (room 1401, E6-1, KAIST)

On page 335 in his lost notebook, Ramanujan recorded without proofs two identities involving finite trigonometric sums and doubly infinite series of Bessel functions. We proved each of these identities under three different interpretations for the double series, and showed that they are intimately connected with the classical circle and divisor problems in number theory. Furthermore, we established many analogues and generalizations of them. This is joint work with Bruce C. Berndt and Alexandru Zaharescu.