In this Note, we give an explicit geometric formula for twisted orbital integrals using the method of the hypoelliptic Laplacian developed by Bismut. We apply this formula to evaluate the leading term in the asymptotic expansion of the equivariant Ray–Singer analytic torsion on compact locally symmetric spaces.
On donne une formule géométrique explicite pour des intégrales orbitales tordues en utilisant la méthode du laplacien hypoelliptique développée par Bismut. On utilise cette formule explicite pour évaluer le terme dominant dans l'asymptotique de la torsion équivariante de Ray–Singer sur un espace localement symétrique compact.
Accepted:
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Bingxiao Liu 1
@article{CRMATH_2019__357_1_74_0,
author = {Bingxiao Liu},
title = {Hypoelliptic {Laplacian} and twisted trace formula},
journal = {Comptes Rendus. Math\'ematique},
pages = {74--83},
publisher = {Elsevier},
volume = {357},
number = {1},
year = {2019},
doi = {10.1016/j.crma.2018.11.010},
language = {en},
}
Bingxiao Liu. Hypoelliptic Laplacian and twisted trace formula. Comptes Rendus. Mathématique, Volume 357 (2019) no. 1, pp. 74-83. doi : 10.1016/j.crma.2018.11.010. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.11.010/
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