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Funktsional'nyi Analiz i ego Prilozheniya, 2012, Volume 46, Issue 2, Pages 66–82
DOI: https://doi.org/10.4213/faa3073 (Mi faa3073) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Explicit Formula for the Spectral Counting Function of the Laplace Operator on a Compact Riemannian Surface of Genus $g>1$

D. A. Popovab

a M. V. Lomonosov Moscow State University
b A. N. Belozersky Institute of Physico-Chemical Biology, M. V. Lomonosov Moscow State University
Full-text PDF (235 kB) Citations (3)
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DOI: https://doi.org/10.4213/faa3073
Abstract: Let the standard Riemannian metric of constant curvature $K=-1$ be given on a compact Riemannian surface of genus $g>1$. Under this condition, for a class of strictly hyperbolic Fuchsian groups, we obtain an explicit expression for the spectral counting function of the Laplace operator in the form of a series over the zeros of the Selberg zeta function.
Keywords: Selberg zeta function, spectral counting function, strictly hyperbolic group.
Received: 24.02.2011
English version:
Functional Analysis and Its Applications, 2012, Volume 46, Issue 2, Pages 133–146
DOI: https://doi.org/10.1007/s10688-012-0019-z
Bibliographic databases:
Document Type: Article
UDC: 517.984.5
Language: Russian
Citation: D. A. Popov, “Explicit Formula for the Spectral Counting Function of the Laplace Operator on a Compact Riemannian Surface of Genus $g>1$”, Funktsional. Anal. i Prilozhen., 46:2 (2012), 66–82; Funct. Anal. Appl., 46:2 (2012), 133–146
Citation in format AMSBIB
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  • https://doi.org/10.4213/faa3073
  • https://www.mathnet.ru/eng/faa/v46/i2/p66
    • This publication is cited in the following 3 articles:
    1. D. A. Popov, “Spectrum of the Laplace operator on closed surfaces”, Russian Math. Surveys, 77:1 (2022), 81–97  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. D. A. Popov, “On the Weyl Formula for the Laplace Operator on Hyperbolic Riemann Surfaces”, Funct. Anal. Appl., 48:2 (2014), 150–153  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    3. D. A. Popov, “On the Selberg Trace Formula for Strictly Hyperbolic Groups”, Funct. Anal. Appl., 47:4 (2013), 290–301  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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    Abstract page:750
    Full-text PDF :255
    References:94
    First page:30
     
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