Zap. Nauchn. Sem. POMI, 2010, Volume 377, Pages 78–90
This article is cited in 1 scientific paper (total in 1 paper)
Towards finite-fold Diophantine representations
St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia
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.
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Journal of Mathematical Sciences (New York), 2010, 171:6, 745–752
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
\paper Towards finite-fold Diophantine representations
\inbook Studies in number theory. Part~10
\serial Zap. Nauchn. Sem. POMI
\jour J. Math. Sci. (N. Y.)
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