Mathematics – Number Theory
Scientific paper
2007-07-10
Mathematics
Number Theory
Second author added. Paper now accepted by Proc AMS
Scientific paper
Descent via an isogeny on an elliptic curve is used to construct two subrings
of the field of rational numbers, which are complementary in a strong sense,
and for which Hilbert's Tenth Problem is undecidable. This method further
develops that of Poonen, who used elliptic divisibility sequences to obtain
undecidability results for some large subrings of the rational numbers.
Eisentraeger Kirsten
Everest Graham
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