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Zapiski Nauchnykh Seminarov POMI, 2018, Volume 469, Pages 7–31 (Mi znsl6600)  
This article is cited in 1 scientific paper (total in 1 paper)

Eisenstein formula and Dirihlet correspondence

D. A. Artyushina, A. L. Smirnovb

a St. Petersburg State University, St. Petersburg, Russia
b St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia
Full-text PDF (297 kB) Citations (1)
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Abstract: We obtain an exact formula for the number of integral points in the system of ellipses related according to Dirichlet with an arbitrary imaginary quadratic field. The relation of this formula to arithmetic Riemann–Roch theorems is discussed. So far it has been known only nine similar formulas. They correspond to the imaginary quadratic fields with the trivial class group.
Key words and phrases: integral point, Riemann–Roch theorem, exact formula, ellipse, arithmetic.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00750
Received: 01.09.2018
English version:
Journal of Mathematical Sciences (New York), 2019, Volume 242, Issue 4, Pages 470–486
DOI: https://doi.org/10.1007/s10958-019-04491-8
Bibliographic databases:
Document Type: Article
UDC: 511.2
Language: Russian
Citation: D. A. Artyushin, A. L. Smirnov, “Eisenstein formula and Dirihlet correspondence”, Algebra and number theory. Part 1, Zap. Nauchn. Sem. POMI, 469, POMI, St. Petersburg, 2018, 7–31; J. Math. Sci. (N. Y.), 242:4 (2019), 470–486
Citation in format AMSBIB
\Bibitem{ArtSmi18}
\by D.~A.~Artyushin, A.~L.~Smirnov
\paper Eisenstein formula and Dirihlet correspondence
\inbook Algebra and number theory. Part~1
\serial Zap. Nauchn. Sem. POMI
\yr 2018
\vol 469
\pages 7--31
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6600}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2019
\vol 242
\issue 4
\pages 470--486
\crossref{https://doi.org/10.1007/s10958-019-04491-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85072114138}
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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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