Affine curves with infinitely many integral points
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- by Dimitrios Poulakis PDF
- Proc. Amer. Math. Soc. 131 (2003), 1357-1359 Request permission
Abstract:
Let $C \subset {\mathbf {A}}^{n}$ be an irreducible affine curve of (geometric) genus 0 defined by a finite family of polynomials having integer coefficients. In this note we give a necessary and sufficient condition for $C$ to possess infinitely many integer points, correcting a statement of J. H. Silverman (Theoret. Comput. Sci., 2000).References
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- Joseph H. Silverman, On the distribution of integer points on curves of genus zero, Theoret. Comput. Sci. 235 (2000), no. 1, 163–170. Selected papers in honor of Manuel Blum (Hong Kong, 1998). MR 1765971, DOI 10.1016/S0304-3975(99)00189-9
Additional Information
- Dimitrios Poulakis
- Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
- Email: poulakis@auth.gr
- Received by editor(s): March 19, 2001
- Received by editor(s) in revised form: January 8, 2002
- Published electronically: October 1, 2002
- Communicated by: Michael Stillman
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1357-1359
- MSC (2000): Primary 11G30, 14G25, 11D41
- DOI: https://doi.org/10.1090/S0002-9939-02-06841-7
- MathSciNet review: 1949864