The number of solutions of a diophantine equation over a recursive ring
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Abstract:
Let $R$ be a recursive ring whose quotient field is not algebraically closed with the property that Hilbert’s Tenth Problem over $R$ is undecidable, and let $A$ be a non-empty proper subset of $\{0,1,2,\ldots \}\cup \{\aleph _0\}$. We prove that it is not decidable whether the number of solutions of a diophantine equation with coefficients in $R$ is in $A$.References
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Additional Information
- Christoph Baxa
- Affiliation: Department of Mathematics, University of Vienna, Nordbergstraße 15, A–1090 Wien, Austria
- Email: christoph.baxa@univie.ac.at
- Received by editor(s): December 1, 2011
- Received by editor(s) in revised form: February 12, 2012
- Published electronically: August 20, 2013
- Communicated by: Julia Knight
- © Copyright 2013 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 141 (2013), 4175-4178
- MSC (2010): Primary 11U05; Secondary 03B25, 11D45
- DOI: https://doi.org/10.1090/S0002-9939-2013-11698-9
- MathSciNet review: 3105860