Descent on elliptic curves and Hilbert’s tenth problem
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- by Kirsten Eisenträger and Graham Everest PDF
- Proc. Amer. Math. Soc. 137 (2009), 1951-1959 Request permission
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.References
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Additional Information
- Kirsten Eisenträger
- Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
- MR Author ID: 717302
- Email: eisentra@math.psu.edu
- Graham Everest
- Affiliation: School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom
- Email: g.everest@uea.ac.uk
- Received by editor(s): October 9, 2007
- Received by editor(s) in revised form: August 28, 2008
- Published electronically: December 18, 2008
- Additional Notes: The authors thank the ICMS in Edinburgh for the workshop on Number Theory and Computability in 2007 funded by EPSRC and the LMS
The first author was partially supported by NSF grant DMS-0801123 and a grant from the John Templeton Foundation. - Communicated by: Ken Ono
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1951-1959
- MSC (2000): Primary 11G05, 11U05
- DOI: https://doi.org/10.1090/S0002-9939-08-09740-2
- MathSciNet review: 2480276