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Matematicheskie Zametki, 2019, Volume 105, Issue 2, Pages 278–293
DOI: https://doi.org/10.4213/mzm12254 (Mi mzm12254) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Singular Functions in the Problem of the Weighted Number of Integer Points on Multidimensional Hyperboloids of Special Form

U. M. Pachev, R. A. Dokhov

Kabardino-Balkar State University, Nal'chik
Full-text PDF (523 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm12254
Abstract: The paper is devoted to the application of the circle method to the problem of an asymptotics of the weighted number of integer points on multidimensional hyperboloids of a special form. We prove the convergence and positivity of the singular series and obtain an asymptotic formula for the singular integral of this problem. Earlier, only estimates for the singular integral were known.
Keywords: circle method, weighted number of integer points, multidimensional hyperboloid, double Gauss sum, singular series, singular integral, Ramanujan sum.
Received: 26.06.2018
English version:
Mathematical Notes, 2019, Volume 105, Issue 2, Pages 265–279
DOI: https://doi.org/10.1134/S0001434619010292
Bibliographic databases:
Document Type: Article
UDC: 511.3
Language: Russian
Citation: U. M. Pachev, R. A. Dokhov, “Singular Functions in the Problem of the Weighted Number of Integer Points on Multidimensional Hyperboloids of Special Form”, Mat. Zametki, 105:2 (2019), 278–293; Math. Notes, 105:2 (2019), 265–279
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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