The twisted Selberg trace formula and the twisted Selberg zeta function for compact orbifolds

被引：0
作者：
Ksenia Fedosova
机构：
[1] Albert-Ludwigs-Universität Freiburg,
[2] Mathematisches Institut,undefined
来源：
Mathematische Zeitschrift | 2023年 / 305卷
关键词：
Selberg trace formula; Selberg zeta function; Spectral theory; 11F72; 11M36;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We propose a version of the Selberg trace formula for compact hyperbolic orbifolds Γ\H2n+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma \backslash {\mathbb {H}}^{2n+1}$$\end{document} for non-unitary representations of Γ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document} and establish that the associated Selberg zeta function admits a meromorphic continuation to C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {C}}$$\end{document}.
引用
收藏
相关论文
共 14 条
  • [1] Farsi C(2001)Orbifold spectral theory Rocky Mount. J. Math. 31 215-236
  • [2] Gon Y(2010)The zeta functions of Ruelle and Selberg for hyperbolic manifolds with cusps Math. Ann. 346 719-767
  • [3] Park J(2012)Classical and quantum ergodicity on orbifolds Russ. J. Math. Phys. 19 307-316
  • [4] Kordyukov YA(1980)The Minakshisundaram-Pleijel coefficients for the vector-valued heat kernel on compact locally symmetric spaces of negative curvature Trans. Am. Math. Soc. 260 1-33
  • [5] Miatello RJ(2012)Analytic torsion of complete hyperbolic manifolds of finite volume J. Funct. Anal. 263 2615-2675
  • [6] Müller W(1989)Eta invariants of Dirac operators on locally symmetric manifolds Invent. Math. 95 629-666
  • [7] Pfaff J(2011)A Selberg trace formula for non-unitary twists Int. Math. Res. Not. 2011 2068-2109
  • [8] Moscovici H(1956)Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series J. Indian Math. Soc. 20 47-87
  • [9] Stanton RJ(1973)The Fourier transform on semi-simple Lie groups of real rank one Acta Math. 131 1-26
  • [10] Müller W(1993)On the Selberg trace formula in the case of compact quotient Represent. Theory Automorph. Forms 2 283-undefined
12