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Zapiski Nauchnykh Seminarov POMI, 1995, Volume 227, Pages 5–8 (Mi znsl4257)  

This article is cited in 1 scientific paper (total in 1 paper)

Computation of the number of representations of the elements of the ring $\mathbb Z/d\mathbb Z$ as a sum of squares

G. V. Abramov, P. M. Vinnik

Saint-Petersburg State University
Full-text PDF (192 kB) Citations (1)
Abstract: The number of representations of the elements of the ring $\mathbb Z/d\mathbb Z$ as a sum of invertible squares is computed, provided that each square occurs in the sum no more than a fixed number of times. For prime $d$ an exhaustive answer is given in terms of the class number and the fundamental unit of the real quadratic field $\mathbb Q(\sqrt d)$. Bibliography: 5 titles.
Received: 15.01.1995
English version:
Journal of Mathematical Sciences (New York), 1998, Volume 89, Issue 2, Pages 1079–1081
DOI: https://doi.org/10.1007/BF02355851
Bibliographic databases:
Document Type: Article
UDC: 511.23
Language: Russian
Citation: G. V. Abramov, P. M. Vinnik, “Computation of the number of representations of the elements of the ring $\mathbb Z/d\mathbb Z$ as a sum of squares”, Problems in the theory of representations of algebras and groups. Part 4, Zap. Nauchn. Sem. POMI, 227, POMI, St. Petersburg, 1995, 5–8; J. Math. Sci. (New York), 89:2 (1998), 1079–1081
Citation in format AMSBIB
\Bibitem{AbrVin95}
\by G.~V.~Abramov, P.~M.~Vinnik
\paper Computation of the number of representations of the elements of the ring $\mathbb Z/d\mathbb Z$ as a~sum of squares
\inbook Problems in the theory of representations of algebras and groups. Part~4
\serial Zap. Nauchn. Sem. POMI
\yr 1995
\vol 227
\pages 5--8
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4257}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1374551}
\zmath{https://zbmath.org/?q=an:0898.11012|0894.11014}
\transl
\jour J. Math. Sci. (New York)
\yr 1998
\vol 89
\issue 2
\pages 1079--1081
\crossref{https://doi.org/10.1007/BF02355851}
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  • https://www.mathnet.ru/eng/znsl/v227/p5
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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