Abstract
This paper begins a new approach to the r-trace formula, without removing the nontempered contribution to the spectral side. We first establish an invariant trace formula whose discrete spectral terms are weighted by automorphic L-functions. This involves extending the results of Finis, Lapid, and Müller on the continuity of the coarse expansion of Arthur’s noninvariant trace formula to the refined expansion, and then to the invariant trace formula, while incorporating the use of basic functions at unramified places.
Résumé
Cet article propose une nouvelle approche de la formule de r-trace, sans supprimer la contribution non-tempérée au côté spectral. Nous établissons d’abord une formule de trace invariante dont les termes spectraux discrets sont pondérés par des fonctions-L automorphes. Cela implique d’étendre les résultats de Finis, Lapid et Müller sur la continuité du développement grossier de la formule de trace non-invariante d’Arthur au développement raffiné, puis à la formule de trace invariante, tout en utilisant les fonctions de base à des places non-ramifiés.
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Wong, T.A. A weighted invariant trace formula. Ann. Math. Québec 48, 79–112 (2024). https://doi.org/10.1007/s40316-022-00200-1
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DOI: https://doi.org/10.1007/s40316-022-00200-1