Geodesic
Eisenstein series and the trace formula for $\mathrm{GL}(2)$ over a function field
Documenta mathematica, Tome 19 (2014), pp. 1-62
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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 OX​-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.
DOI : 10.4171/dm/439
Classification : 11F70, 11F72, 11G20, 11R39, 11R52, 11R58, 11S37, 14H30, 22E35, 22E55
Mots-clés : automorphic representations, function fields, Eisenstein series, intertwining operators, trace formula, GL(2), orbital integrals 
@article{10_4171_dm_439,
     author = {Yuval Z. Flicker},
     title = {Eisenstein series and the trace formula for $\mathrm{GL}(2)$ over a function field},
     journal = {Documenta mathematica},
     pages = {1--62},
     year = {2014},
     volume = {19},
     doi = {10.4171/dm/439},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/439/}
}
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Yuval Z. Flicker. Eisenstein series and the trace formula for $\mathrm{GL}(2)$ over a function field. Documenta mathematica, Tome 19 (2014), pp. 1-62. doi: 10.4171/dm/439

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