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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
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
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
Linking options:
https://www.mathnet.ru/eng/mzm12254https://doi.org/10.4213/mzm12254 https://www.mathnet.ru/eng/mzm/v105/i2/p278
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Abstract page: | 365 | Full-text PDF : | 24 | References: | 53 | First page: | 25 |
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