The semiclassical zeta function for geodesic flows on negatively curved manifolds

Frédéric Faure, Tsujii Masato

研究成果: ジャーナルへの寄稿記事

7 引用 (Scopus)

抄録

We consider the semi-classical (or Gutzwiller–Voros) zeta functions for C contact Anosov flows. Analyzing the spectra of the generators of some transfer operators associated to the flow, we prove that, for arbitrarily small τ> 0 , its zeros are contained in the union of the τ-neighborhood of the imaginary axis, | R(s) | < τ, and the half-plane R(s) < - χ0+ τ, up to finitely many exceptions, where χ0> 0 is the hyperbolicity exponent of the flow. Further we show that the density of the zeros along the imaginary axis satisfy an analogue of the Weyl law.

元の言語英語
ページ(範囲)851-998
ページ数148
ジャーナルInventiones Mathematicae
208
発行部数3
DOI
出版物ステータス出版済み - 6 1 2017

Fingerprint

Geodesic Flow
Riemann zeta function
Anosov Flow
Transfer Operator
Hyperbolicity
Zero
Union
Exponent
Generator
Contact
Analogue

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

これを引用

The semiclassical zeta function for geodesic flows on negatively curved manifolds. / Faure, Frédéric; Masato, Tsujii.

:: Inventiones Mathematicae, 巻 208, 番号 3, 01.06.2017, p. 851-998.

研究成果: ジャーナルへの寄稿記事

@article{7db6923f4a8c404f9def9dfc9a9c0ca4,
title = "The semiclassical zeta function for geodesic flows on negatively curved manifolds",
abstract = "We consider the semi-classical (or Gutzwiller–Voros) zeta functions for C∞ contact Anosov flows. Analyzing the spectra of the generators of some transfer operators associated to the flow, we prove that, for arbitrarily small τ> 0 , its zeros are contained in the union of the τ-neighborhood of the imaginary axis, | R(s) | < τ, and the half-plane R(s) < - χ0+ τ, up to finitely many exceptions, where χ0> 0 is the hyperbolicity exponent of the flow. Further we show that the density of the zeros along the imaginary axis satisfy an analogue of the Weyl law.",
author = "Fr{\'e}d{\'e}ric Faure and Tsujii Masato",
year = "2017",
month = "6",
day = "1",
doi = "10.1007/s00222-016-0701-5",
language = "English",
volume = "208",
pages = "851--998",
journal = "Inventiones Mathematicae",
issn = "0020-9910",
publisher = "Springer New York",
number = "3",

}

TY - JOUR

T1 - The semiclassical zeta function for geodesic flows on negatively curved manifolds

AU - Faure, Frédéric

AU - Masato, Tsujii

PY - 2017/6/1

Y1 - 2017/6/1

N2 - We consider the semi-classical (or Gutzwiller–Voros) zeta functions for C∞ contact Anosov flows. Analyzing the spectra of the generators of some transfer operators associated to the flow, we prove that, for arbitrarily small τ> 0 , its zeros are contained in the union of the τ-neighborhood of the imaginary axis, | R(s) | < τ, and the half-plane R(s) < - χ0+ τ, up to finitely many exceptions, where χ0> 0 is the hyperbolicity exponent of the flow. Further we show that the density of the zeros along the imaginary axis satisfy an analogue of the Weyl law.

AB - We consider the semi-classical (or Gutzwiller–Voros) zeta functions for C∞ contact Anosov flows. Analyzing the spectra of the generators of some transfer operators associated to the flow, we prove that, for arbitrarily small τ> 0 , its zeros are contained in the union of the τ-neighborhood of the imaginary axis, | R(s) | < τ, and the half-plane R(s) < - χ0+ τ, up to finitely many exceptions, where χ0> 0 is the hyperbolicity exponent of the flow. Further we show that the density of the zeros along the imaginary axis satisfy an analogue of the Weyl law.

UR - http://www.scopus.com/inward/record.url?scp=84996968538&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84996968538&partnerID=8YFLogxK

U2 - 10.1007/s00222-016-0701-5

DO - 10.1007/s00222-016-0701-5

M3 - Article

VL - 208

SP - 851

EP - 998

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 3

ER -