Zapiski Nauchnykh Seminarov POMI
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zap. Nauchn. Sem. POMI:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Zap. Nauchn. Sem. POMI, 2010, Volume 377, Pages 78–90 (Mi znsl3816)  

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

Towards finite-fold Diophantine representations

Yu. Matiyasevich

St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia

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.

Full text: PDF file (606 kB)
References: PDF file   HTML file

English version:
Journal of Mathematical Sciences (New York), 2010, 171:6, 745–752

UDC: 511.5+510.53
Received: 10.05.2010
Language:

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}


Linking options:
  • http://mi.mathnet.ru/eng/znsl3816
  • http://mi.mathnet.ru/eng/znsl/v377/p78

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Tyszka A., “Mupad Codes Which Implement Limit-Computable Functions That Cannot Be Bounded By Any Computable Function”, Federated Conference on Computer Science and Information Systems, 2014, Acsis-Annals of Computer Science and Information Systems, 2, IEEE, 2014, 623–629  crossref  isi  scopus
  • Записки научных семинаров ПОМИ
    Number of views:
    This page:301
    Full text:100
    References:34

     
    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2022