Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion

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Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion. / Matz, Jasmin; Müller, Werner.

I: Journal of Functional Analysis, Bind 284, Nr. 1, 109727, 2023.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Matz, J & Müller, W 2023, 'Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion', Journal of Functional Analysis, bind 284, nr. 1, 109727. https://doi.org/10.1016/j.jfa.2022.109727

APA

Matz, J., & Müller, W. (2023). Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion. Journal of Functional Analysis, 284(1), [109727]. https://doi.org/10.1016/j.jfa.2022.109727

Vancouver

Matz J, Müller W. Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion. Journal of Functional Analysis. 2023;284(1). 109727. https://doi.org/10.1016/j.jfa.2022.109727

Author

Matz, Jasmin ; Müller, Werner. / Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion. I: Journal of Functional Analysis. 2023 ; Bind 284, Nr. 1.

Bibtex

@article{c2a1b0e630ac493aa3b7e07c00c9aade,
title = "Analytic torsion for arithmetic locally symmetric manifolds and approximation of L2-torsion",
abstract = "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.",
keywords = "Analytic torsion, Locally symmetric spaces",
author = "Jasmin Matz and Werner M{\"u}ller",
note = "Publisher Copyright: {\textcopyright} 2022 The Author(s)",
year = "2023",
doi = "10.1016/j.jfa.2022.109727",
language = "English",
volume = "284",
journal = "Journal of Functional Analysis",
issn = "0022-1236",
publisher = "Academic Press",
number = "1",

}

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