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.
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.
Accepted:
Published online:
@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 = {https://www.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 - https://www.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 https://www.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, Volume 354 (2016) no. 4, pp. 433-436. doi : 10.1016/j.crma.2016.01.008. https://www.numdam.org/articles/10.1016/j.crma.2016.01.008/
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