The Langlands lemma and the Betti numbers of stacks of $G$--bundles on a curve

@article{Laumon1995TheLL,
  title={The Langlands lemma and the Betti numbers of stacks of \$G\$--bundles on a curve},
  author={G'erard Laumon and Michael Rapoport},
  journal={arXiv: Algebraic Geometry},
  year={1995}
}
In this note we show that the Langlands lemma from the theory of Eisenstein series can be used to invert the recursion relation for the Poincar\'e series of the open substack of semi-stable $G$-bundles which was established by Atiyah/Bott and Harder/Narasimhan. 
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