Descent on elliptic curves and hilbert's tenth problem

Kirsten Eisenträger; Graham Everest

doi:10.1090/S0002-9939-08-09740-2

Descent on elliptic curves and hilbert's tenth problem

Kirsten Eisenträger, Graham Everest

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

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.

Original language	English (US)
Pages (from-to)	1951-1959
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	6
DOIs	https://doi.org/10.1090/S0002-9939-08-09740-2
State	Published - Jun 2009

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-08-09740-2

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Descent on elliptic curves and hilbert's tenth problem

Abstract

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