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Determining Integer-Valued Polynomials From Their Image
Vadim Ponomarenko1
1 San Diego State University Department of Mathematics and Statistics San Diego, CA 92182-7720
Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 51-52.

This note summarizes a presentation made at the Third International Meeting on Integer Valued Polynomials and Problems in Commutative Algebra. All the work behind it is joint with Scott T. Chapman, and will appear in [2]. Let Int(ℤ) represent the ring of polynomials with rational coefficients which are integer-valued at integers. We determine criteria for two such polynomials to have the same image set on ℤ.

Published online:
DOI: 10.5802/acirm.33
Classification: 13F05, 11C08, 13F20, 13G05, 13B25
Keywords: integer-valued polynomial
Vadim Ponomarenko 1

1 San Diego State University Department of Mathematics and Statistics San Diego, CA 92182-7720 
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Vadim Ponomarenko. Determining Integer-Valued Polynomials From Their Image. Actes des rencontres du CIRM, Volume 2 (2010) no. 2, pp. 51-52. doi : 10.5802/acirm.33. https://pmb.cedram.org/articles/10.5802/acirm.33/

[1] Paul-Jean Cahen, Jean-Luc Chabert, and Sophie Frisch, Interpolation domains, J. Algebra 225 (2000), no. 2, 794–803. MR 1741562 (2001b:13024) | DOI | MR | Zbl

[2] Scott T. Chapman and Vadim Ponomarenko, On image sets of integer-valued polynomials, submitted. | DOI | MR | Zbl

[3] Sophie Frisch, Interpolation by integer-valued polynomials, J. Algebra 211 (1999), no. 2, 562–577. MR 1666659 (99m:13016) | DOI | MR | Zbl

[4] G. Peruginelli and U. Zannier, Parametrizing over ℤ integral values of polynomials over ℚ, Comm. Algebra 38 (2010), no. 1, 119–130. MR 2597485 (2011e:11064) | DOI | Zbl

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