Proceedings of the American Mathematical Society

Author(s): Kirsten Eisenträger; Graham Everest
Journal: Proc. Amer. Math. Soc. 137 (2009), 1951-1959.
MSC (2000): Primary 11G05, 11U05
Posted: December 18, 2008
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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.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11G05, 11U05

Kirsten Eisenträger
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802
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

DOI: 10.1090/S0002-9939-08-09740-2
PII: S 0002-9939(08)09740-2
Keywords: Elliptic curve, elliptic divisibility sequence, Hilbert's Tenth Problem, isogeny, primitive divisor, $S$-integers, undecidability
Received by editor(s): October 9, 2007,
Received by editor(s) in revised form: August 28, 2008
Posted: 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 of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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