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Diophantine representation of Mersenne and Fermat primes

James Jones (1979)

Acta Arithmetica

Diophantine Undecidability of Holomorphy Rings of Function Fields of Characteristic 0

Laurent Moret-Bailly, Alexandra Shlapentokh (2009)

Annales de l’institut Fourier

Let $K$ be a one-variable function field over a field of constants of characteristic 0. Let $R$ be a holomorphy subring of $K$ , not equal to $K$ . We prove the following undecidability results for $R$ : if $K$ is recursive, then Hilbert’s Tenth Problem is undecidable in $R$ . In general, there exist $x_{1}, ..., x_{n} \in R$ such that there is no algorithm to tell whether a polynomial equation with coefficients in $ℚ (x_{1}, ..., x_{n})$ has solutions in $R$ .

Dirichlet theorems and prime number hypotheses of a conditional Goldbach theorem.

H.A. Pogorzelski (1976)

Journal für die reine und angewandte Mathematik

Disconnectedness of Sublevel Sets of Some Riemannian.

A. Nabutovsky (1996)

Geometric and functional analysis

Disjunction in modal description logics.

Mosurović, Milenko (2007)

Publications de l'Institut Mathématique. Nouvelle Série