Articles written in Proceedings – Mathematical Sciences
Volume 90 Issue 2 May 1981 pp 129-149
Volume 93 Issue 2-3 December 1984 pp 147-160
Recently, Bombieri and Vaaler obtained an interesting adelic formulation of the first and the second theorems of Minkowski in the Geometry of Numbers and derived an effective formulation of the well-known “Siegel’s lemma” on the size of integral solutions of linear equations. In a similar context involving linear
Volume 97 Issue 1-3 December 1987 pp 263-276
For Ramanujan’s modular identities connected with his well-known partition congruences for the moduli 5 or 7, we had given, in an earlier paper, natural and uniform proofs through the medium of modular forms. Analogous (modular) identities corresponding to the (more difficult) case of the modulus 11 are provided here, with the consequent partition congruences; the relationship with relevant results of N J Fine is also sketched.
Volume 104 Issue 1 February 1994 pp 77-92 Obituary note
In this article we establish the analogue of a theorem of Kuznetsov (theorem 6 of ) in the case of 3-dimensional hyperbolic space. We also consider a generalization of this result for higher dimensional hyperbolic spaces and discuss the relevant ingredients of a proof.