SUPERCUSPIDAL REPRESENTATIONS AND POINCARE-SERIES OVER FUNCTION-FIELDS

In this paper, we will give a new construction of certain cusp forms on GL(2) over a rational function field. The forms which we construct are analogs of holomorphic modular forms, in that the local representations at the infinite place are in the discrete series. The novelty of our approach is that we are able to give a very explicit construction of these forms as certain 'Poincare series.' We will also study the exponential sums which arise in the Fourier expansions of these Poincare series.