Dipendra Prasad

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We give a conjectural description of the restriction of an irreducible representation of a unitary group U(n) to a subgroup U(n − 1) over a local or global field. We formulate analogous conjectures for the restriction problem from U(n) to a subgroup U(m) (m < n) using Bessel and Fourier-Jacobi models, and also similar restriction problems for symplectic(More)
We prove several multiplicity one theorems in this paper. For k a local field not of characteristic two, and V a symplectic space over k, any irreducible admissible representation of the symplectic similitude group GSp(V ) decomposes with multiplicity one when restricted to the symplectic group Sp(V ). We prove the analogous result for GO(V ) and O(V ),(More)
Let E be an elliptic curve defined over Q. Let E(Fp) denote the elliptic curve modulo p. It is known that there exist integers i p and f p such that E(Fp) ∼= Z/ i pZ × Z/ i p f pZ. We study questions related to i p and f p . In particular, for any α > 0 and k ∈ N, we prove there exist positive constants cα and ck such that for any A > 0 ∑ p≤x (log i p) α =(More)
In this paper we study the theta correspondence for Unitary groups of the same size over local and global fields. This correspondence has been studied in many cases by several authors. We are able to unify and generalise all these known results in terms of two conjectures, one local and the other global. These conjectures are in terms of the parametrisation(More)