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Izvestiya: Mathematics, 2020, Volume 84, Issue 5, Pages 960–977
DOI: https://doi.org/10.1070/IM8999 (Mi im8999) 		 
Distribution of prime numbers and the discrete spectrum of the Laplace operator

D. A. Popov

Lomonosov Moscow State University, Belozersky Research Institute of Physico-Chemical Biology
English version PDF (473 kB) Russian version article
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DOI: https://doi.org/10.1070/IM8999
Abstract: We obtain a class of explicit formulae each of which gives an expression for the remainder term in the asymptotic equation for the Chebyshev function in terms of the spectrum of the Laplace operator on the fundamental domain of the modular group.
Keywords: prime numbers, Chebyshev psi-function, spectrum of the Laplace operator, modular group.
Received: 05.12.2019
Bibliographic databases:
Document Type: Article
UDC: 511.331+515.178.1
MSC: Primary 58J50; Secondary 11M36
Language: English
Original paper language: Russian
Citation: D. A. Popov, “Distribution of prime numbers and the discrete spectrum of the Laplace operator”, Izv. Math., 84:5 (2020), 960–977
Citation in format AMSBIB
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\by D.~A.~Popov
\paper Distribution of~prime numbers and the discrete spectrum of~the Laplace operator
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\yr 2020
\vol 84
\issue 5
\pages 960--977
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:289
    Russian version PDF:80
    English version PDF:20
    References:45
    First page:25
     
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