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Izvestiya: Mathematics, 2019, Volume 83, Issue 5, Pages 1066–1079
DOI: https://doi.org/10.1070/IM8783 (Mi im8783) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The discrete spectrum of the Laplace operator on the fundamental domain of the modular group and the Chebyshev psi-function

D. A. Popov

Lomonosov Moscow State University, Belozersky Research Institute of Physico-Chemical Biology
English version PDF (460 kB) Citations (2)
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DOI: https://doi.org/10.1070/IM8783
Abstract: An explicit formula is obtained expressing the Chebyshev psi-function in terms of the discrete spectrum of the Laplace operator on the fundamental domain of the modular group.
Keywords: Selberg formula, spectrum of the Laplace operator, Chebyshev psi-function, modular group.
Received: 07.03.2018
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2019, Volume 83, Issue 5, Pages 167–180
DOI: https://doi.org/10.4213/im8783
Bibliographic databases:
Document Type: Article
UDC: 511.331+515.178.1
MSC: Primary 11M36; Secondary 11F03
Language: English
Original paper language: Russian
Citation: D. A. Popov, “The discrete spectrum of the Laplace operator on the fundamental domain of the modular group and the Chebyshev psi-function”, Izv. RAN. Ser. Mat., 83:5 (2019), 167–180; Izv. Math., 83:5 (2019), 1066–1079
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v83/i5/p167
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:321
    Russian version PDF:36
    English version PDF:17
    References:37
    First page:19
     
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