Eisenstein series and the trace formula for over a function field

  • Yuval Z. Flicker

    The Ohio State University Columbus Ohio 43210 USA and University of Ariel Ariel 40700 Israel
Eisenstein series and the trace formula for $\mathrm{GL}(2)$ over a function field cover
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Abstract

We write out and prove the trace formula for a convolution operator on the space of cusp forms on over the function field 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 is studied in section 2 by means of locally free sheaves of -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.

Cite this article

Yuval Z. Flicker, Eisenstein series and the trace formula for over a function field. Doc. Math. 19 (2014), pp. 1–62

DOI 10.4171/DM/439