L'objet de cette Note est de démontrer une égalité entre la torsion analytique et la valeur en zéro d'une fonction zêta dynamique associée à un fibré vectoriel unitairement plat sur une variété compacte localement symétrique réductive. Nous démontrons aussi une conjecture de Fried.
The purpose of this Note is to prove an identity between the analytic torsion and the value at zero of a dynamical zeta function associated with an acyclic unitarily flat vector bundle on a closed locally symmetric reductive manifold, which solves a conjecture of Fried.
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@article{CRMATH_2016__354_4_433_0, author = {Shen, Shu}, title = {Analytic torsion, dynamical zeta functions and orbital integrals}, journal = {Comptes Rendus. Math\'ematique}, pages = {433--436}, publisher = {Elsevier}, volume = {354}, number = {4}, year = {2016}, doi = {10.1016/j.crma.2016.01.008}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.crma.2016.01.008/} }
TY - JOUR AU - Shen, Shu TI - Analytic torsion, dynamical zeta functions and orbital integrals JO - Comptes Rendus. Mathématique PY - 2016 SP - 433 EP - 436 VL - 354 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2016.01.008/ DO - 10.1016/j.crma.2016.01.008 LA - en ID - CRMATH_2016__354_4_433_0 ER -
%0 Journal Article %A Shen, Shu %T Analytic torsion, dynamical zeta functions and orbital integrals %J Comptes Rendus. Mathématique %D 2016 %P 433-436 %V 354 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2016.01.008/ %R 10.1016/j.crma.2016.01.008 %G en %F CRMATH_2016__354_4_433_0
Shen, Shu. Analytic torsion, dynamical zeta functions and orbital integrals. Comptes Rendus. Mathématique, Tome 354 (2016) no. 4, pp. 433-436. doi : 10.1016/j.crma.2016.01.008. http://archive.numdam.org/articles/10.1016/j.crma.2016.01.008/
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