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Izvestiya: Mathematics, 2000, Volume 64, Issue 2, Pages 343–361
DOI: https://doi.org/10.1070/im2000v064n02ABEH000286 (Mi im286) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On the number of lattice points in three-dimensional solids of revolution

D. A. Popov

M. V. Lomonosov Moscow State University
English version PDF (248 kB) Citations (6)
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DOI: https://doi.org/10.1070/im2000v064n02ABEH000286
Abstract: We derive an accurate estimate for the order of magnitude of the remainder term in the problem of the number of lattice points in families of homothetic domains belonging to the class of three-dimensional solids of revolution with smooth boundaries (under certain additional conditions). This estimate is realized in the case of the solid bounded by a standardly embedded torus, for which the second term of the expansion, which describes the dependence of the number of lattice points on the dilation parameter, is written in explicit form.
Received: 29.09.1998
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2000, Volume 64, Issue 2, Pages 121–140
DOI: https://doi.org/10.4213/im286
Bibliographic databases:
MSC: 11H06, 11P21, 42B10, 42B20
Language: English
Original paper language: Russian
Citation: D. A. Popov, “On the number of lattice points in three-dimensional solids of revolution”, Izv. RAN. Ser. Mat., 64:2 (2000), 121–140; Izv. Math., 64:2 (2000), 343–361
Citation in format AMSBIB
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  • https://doi.org/10.1070/im2000v064n02ABEH000286
  • https://www.mathnet.ru/eng/im/v64/i2/p121
    • This publication is cited in the following 6 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:526
    Russian version PDF:243
    English version PDF:18
    References:68
    First page:1
     
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