Descent on Elliptic Curves and Hilbert's Tenth Problem
Number Theory
2008-10-01 v5 Logic
Abstract
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.
Cite
@article{arxiv.0707.1485,
title = {Descent on Elliptic Curves and Hilbert's Tenth Problem},
author = {Graham Everest and Kirsten Eisentraeger},
journal= {arXiv preprint arXiv:0707.1485},
year = {2008}
}
Comments
Second author added. Paper now accepted by Proc AMS