Eisenstein Series and the trace formula for GL(2) over a Function Field

We write out and prove the trace formula for a convolution operator on the space of cusp forms on GL(2) over the function field F of a smooth projective absolutely irreducible curve over a finite field. The proof - which follows Drinfeld - is complete and all terms in the formula are explicitly computed. The structure of the homogeneous space GL(2, F)\GL(2,A) is studied in section 2 by means of locally free sheaves of O_X-modules. Section 3 deals with the regularization and computation of the geometric terms, over conjugacy classes. Section 4 develops the theory of intertwining operators and Eisenstein Series, and the trace formula is proven in section 5.