Determining Integer-Valued Polynomials From Their Image

Vadim Ponomarenko[1]

  • [1] San Diego State University Department of Mathematics and Statistics San Diego, CA 92182-7720

Actes des rencontres du CIRM (2010)

  • Volume: 2, Issue: 2, page 51-52
  • ISSN: 2105-0597

Abstract

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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 ( ) 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 .

How to cite

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Ponomarenko, Vadim. "Determining Integer-Valued Polynomials From Their Image." Actes des rencontres du CIRM 2.2 (2010): 51-52. <http://eudml.org/doc/196280>.

@article{Ponomarenko2010,
abstract = {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 $\mathrm\{Int\}(\mathbb\{Z\})$ 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 $\mathbb\{Z\}$.},
affiliation = {San Diego State University Department of Mathematics and Statistics San Diego, CA 92182-7720},
author = {Ponomarenko, Vadim},
journal = {Actes des rencontres du CIRM},
keywords = {integer-valued polynomial},
language = {eng},
number = {2},
pages = {51-52},
publisher = {CIRM},
title = {Determining Integer-Valued Polynomials From Their Image},
url = {http://eudml.org/doc/196280},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Ponomarenko, Vadim
TI - Determining Integer-Valued Polynomials From Their Image
JO - Actes des rencontres du CIRM
PY - 2010
PB - CIRM
VL - 2
IS - 2
SP - 51
EP - 52
AB - 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 $\mathrm{Int}(\mathbb{Z})$ 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 $\mathbb{Z}$.
LA - eng
KW - integer-valued polynomial
UR - http://eudml.org/doc/196280
ER -

References

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  1. Paul-Jean Cahen, Jean-Luc Chabert, and Sophie Frisch, Interpolation domains, J. Algebra 225 (2000), no. 2, 794–803. MR 1741562 (2001b:13024) Zbl0990.13014MR1741562
  2. Scott T. Chapman and Vadim Ponomarenko, On image sets of integer-valued polynomials, submitted. Zbl1239.11029
  3. Sophie Frisch, Interpolation by integer-valued polynomials, J. Algebra 211 (1999), no. 2, 562–577. MR 1666659 (99m:13016) Zbl0927.13023MR1666659
  4. G. Peruginelli and U. Zannier, Parametrizing over integral values of polynomials over , Comm. Algebra 38 (2010), no. 1, 119–130. MR 2597485 (2011e:11064) Zbl1219.11048MR2597485

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