Descent on elliptic curves and hilbert's tenth problem

Kirsten Eisenträger, Graham Everest

Research output: Contribution to journalArticle

16 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 languageEnglish (US)
Pages (from-to)1951-1959
Number of pages9
JournalProceedings of the American Mathematical Society
Volume137
Issue number6
DOIs
StatePublished - Jun 1 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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