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Zapiski Nauchnykh Seminarov POMI, 2010, Volume 377, Pages 78–90 (Mi znsl3816)  

This article is cited in 3 scientific papers (total in 3 papers)

Towards finite-fold Diophantine representations

Yu. Matiyasevich

St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia
Full-text PDF (606 kB) Citations (3)
References:
Abstract: Celebrated theorem established by Martin Davis, Hilary Putnam, and Julia Robinson in 1961 states that every effectively enumerable set of natural numbers has an exponential Diophantine representation. This theorem was improved by the author in two ways:
$\bullet$ to the existence of Diophantine representation,
$\bullet$ to the existence of so-called single-fold exponential Diophantine representation.
However, it remains unknown whether these two improvements could be combined, that is, whether every effectively enumerable set has a single-fold (or at least finite-fold) Diophantine representation.
In the paper, we discuss known results about single-fold exponential Diophantine representations, their applications, possible approaches to improving to the case of genuine Diophantine representations, and what would follow if such improvement is impossible. Bibl. 27 titles.
Key words and phrases: single-fold Diophantine represtations, Diophantine equations with finitely many solutions.
Received: 10.05.2010
English version:
Journal of Mathematical Sciences (New York), 2010, Volume 171, Issue 6, Pages 745–752
DOI: https://doi.org/10.1007/s10958-010-0179-4
Bibliographic databases:
Document Type: Article
UDC: 511.5+510.53
Language: English
Citation: Yu. Matiyasevich, “Towards finite-fold Diophantine representations”, Studies in number theory. Part 10, Zap. Nauchn. Sem. POMI, 377, POMI, St. Petersburg, 2010, 78–90; J. Math. Sci. (N. Y.), 171:6 (2010), 745–752
Citation in format AMSBIB
\Bibitem{Mat10}
\by Yu.~Matiyasevich
\paper Towards finite-fold Diophantine representations
\inbook Studies in number theory. Part~10
\serial Zap. Nauchn. Sem. POMI
\yr 2010
\vol 377
\pages 78--90
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl3816}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2010
\vol 171
\issue 6
\pages 745--752
\crossref{https://doi.org/10.1007/s10958-010-0179-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78650073333}
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  • https://www.mathnet.ru/eng/znsl/v377/p78
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Full-text PDF :137
    References:56
     
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