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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 413, Pages 173–182 (Mi znsl5663)  
This article is cited in 2 scientific papers (total in 2 papers)

On exact formulas for the number of integral points

A. Smirnov

Санкт-Петербургское отделение Математического института им. В. А. Стеклова РАН, Фонтанка 27, 191023 Санкт-Петербург, Россия
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Abstract: Exact formulas for the number of integral points in certain ellipses are obtained. These formulas generalize a formula of Eisenstein and belong to a rare type of exact formulas for the number of lattice points in curvilinear domains. The obtained formulas can be useful when studying the Riemann–Roch problem for arithmetic varieties.
Key words and phrases: arithmetic curve, Riemann–Roch theorem, Eisenstein, imaginary quadratic field, exact formula, lattice point.
Received: 20.09.2012
English version:
Journal of Mathematical Sciences (New York), 2014, Volume 202, Issue 3, Pages 448–454
DOI: https://doi.org/10.1007/s10958-014-2054-1
Bibliographic databases:
Document Type: Article
UDC: 511.2
Language: English
Citation: A. Smirnov, “On exact formulas for the number of integral points”, Problems in the theory of representations of algebras and groups. Part 24, Zap. Nauchn. Sem. POMI, 413, POMI, St. Petersburg, 2013, 173–182; J. Math. Sci. (N. Y.), 202:3 (2014), 448–454
Citation in format AMSBIB
\Bibitem{Smi13}
\by A.~Smirnov
\paper On exact formulas for the number of integral points
\inbook Problems in the theory of representations of algebras and groups. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 413
\pages 173--182
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5663}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3073064}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 202
\issue 3
\pages 448--454
\crossref{https://doi.org/10.1007/s10958-014-2054-1}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919922283}
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  • https://www.mathnet.ru/eng/znsl/v413/p173
    • 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
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