Hilbert's Tenth Problem and Mazur's Conjecture for large subrings of $\mathbb{Q}$
By Bjorn Poonen. 2003
53 citations recorded by the source corpus.
We give the first examples of infinite sets of primes S such that Hilbert's Tenth Problem over Z[S^{-1}] has a negative answer. In fact, we can take S to be a density 1 set of primes. We show also that for some such S there is a punctured elliptic curve E' over Z[S^{-1}] such that the topological closure of E'(Z[S^{-1}]) in E'(R) has infinitely many connected components.
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/a6ddcd246c35759b84114aa020caff807e7b4dfb
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In Algebra and Number Theory
In Geometry and Topology
Citations in the corpus
- Most Tensor Problems Are NP-Hard (2009, background): “et of quadratics whose solvability over Z encodes whether a given Turing machine halts. The decidability of Problem 2.1 with F = Q is still unknown, as is the general Diophantine problem over Q. See [Poonen 2003] for some recent progress on this dicult problem. While a system of quadratic equations ”