Descent on elliptic curves and hilbert's tenth problem

Kirsten Eisenträger, Graham Everest

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


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 languageEnglish (US)
Pages (from-to)1951-1959
Number of pages9
JournalProceedings of the American Mathematical Society
Issue number6
StatePublished - Jun 2009

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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