Geodesic
Eisenstein series and the trace formula for $\mathrm{GL}(2)$ over a function field
Documenta mathematica, Tome 19 (2014), pp. 1-62.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 $\GL(2,F)\bs\GL(2,\A)$ is studied in section 2 by means of locally free sheaves of $\OO_X$-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.
Classification : 11F70, 11F72, 22E35, 22E55, 11G20, 11R39, 11R52, 11R58, 14H30, 11S37
Keywords: Eisenstein series, intertwining operators, trace formula, automorphic representations, $GL(2)$, function fields, orbital integrals 
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     author = {Flicker, Yuval Z.},
     title = {Eisenstein series and the trace formula for $\mathrm{GL}(2)$ over a function field},
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     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a44/}
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Flicker, Yuval Z. Eisenstein series and the trace formula for $\mathrm{GL}(2)$ over a function field. Documenta mathematica, Tome 19 (2014), pp. 1-62. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a44/