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Zapiski Nauchnykh Seminarov POMI, 1995, Volume 220, Pages 36–48 (Mi znsl4279)  
This article is cited in 2 scientific papers (total in 2 papers)

Infinite sets of primes, admitting Diophantine representations in eight variables

M. A. Vsemirnov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (560 kB) Citations (2)
Abstract: The existence of infinite sets of primes which can be repesented as the sets of positive values of some polynomials in a small number of variables is discussed. (All variables range over positive integers.) It is proved (noneffectively) that there exists such a set, which has a representation with eight variables. This number of variables is smaller than in the best universal construction known today, which is ten. Also, some improvements of well-known technical lemmas are given. Bibliography: 16 titles.
Received: 25.02.1994
English version:
Journal of Mathematical Sciences (New York), 1997, Volume 87, Issue 1, Pages 3200–3208
DOI: https://doi.org/10.1007/BF02358993
Bibliographic databases:
Document Type: Article
UDC: 511.5+511.2
Language: Russian
Citation: M. A. Vsemirnov, “Infinite sets of primes, admitting Diophantine representations in eight variables”, Studies in constructive mathematics and mathematical logic. Part IX, Zap. Nauchn. Sem. POMI, 220, POMI, St. Petersburg, 1995, 36–48; J. Math. Sci. (New York), 87:1 (1997), 3200–3208
Citation in format AMSBIB
\Bibitem{Vse95}
\by M.~A.~Vsemirnov
\paper Infinite sets of primes, admitting Diophantine representations in eight variables
\inbook Studies in constructive mathematics and mathematical logic. Part~IX
\serial Zap. Nauchn. Sem. POMI
\yr 1995
\vol 220
\pages 36--48
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4279}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1374094}
\zmath{https://zbmath.org/?q=an:0932.11078}
\transl
\jour J. Math. Sci. (New York)
\yr 1997
\vol 87
\issue 1
\pages 3200--3208
\crossref{https://doi.org/10.1007/BF02358993}
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  • https://www.mathnet.ru/eng/znsl/v220/p36
    • 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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