Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion
Research output: Contribution to journal › Journal article › Research › peer-review
Standard
Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion. / Matz, Jasmin; Müller, Werner.
In: Journal of Functional Analysis, Vol. 284, No. 1, 109727, 2023.Research output: Contribution to journal › Journal article › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
TY - JOUR
T1 - Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion
AU - Matz, Jasmin
AU - Müller, Werner
N1 - Publisher Copyright: © 2022 The Author(s)
PY - 2023
Y1 - 2023
N2 - In this paper we define a regularized version of the analytic torsion for quotients of a symmetric space of non-positive curvature by arithmetic lattices. The definition is based on the study of the renormalized trace of the corresponding heat operators, which is defined as the geometric side of the Arthur trace formula applied to the heat kernel. Then we study the limiting behavior of the analytic torsion as the lattices run through a sequence of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for sequences of principal congruence subgroups, which converge to 1 at a fixed finite set of places and strongly acyclic flat bundles, the logarithm of the analytic torsion, divided by the index of the subgroup, converges to the L2-analytic torsion.
AB - In this paper we define a regularized version of the analytic torsion for quotients of a symmetric space of non-positive curvature by arithmetic lattices. The definition is based on the study of the renormalized trace of the corresponding heat operators, which is defined as the geometric side of the Arthur trace formula applied to the heat kernel. Then we study the limiting behavior of the analytic torsion as the lattices run through a sequence of congruence subgroups of a fixed arithmetic subgroup. Our main result states that for sequences of principal congruence subgroups, which converge to 1 at a fixed finite set of places and strongly acyclic flat bundles, the logarithm of the analytic torsion, divided by the index of the subgroup, converges to the L2-analytic torsion.
KW - Analytic torsion
KW - Locally symmetric spaces
U2 - 10.1016/j.jfa.2022.109727
DO - 10.1016/j.jfa.2022.109727
M3 - Journal article
AN - SCOPUS:85139731408
VL - 284
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 1
M1 - 109727
ER -
ID: 371656103