# 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

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topPonomarenko, 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

top- 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
- Scott T. Chapman and Vadim Ponomarenko, On image sets of integer-valued polynomials, submitted. Zbl1239.11029
- Sophie Frisch, Interpolation by integer-valued polynomials, J. Algebra 211 (1999), no. 2, 562–577. MR 1666659 (99m:13016) Zbl0927.13023MR1666659
- G. Peruginelli and U. Zannier, Parametrizing over $\mathbb{Z}$ integral values of polynomials over $\mathbb{Q}$, Comm. Algebra 38 (2010), no. 1, 119–130. MR 2597485 (2011e:11064) Zbl1219.11048MR2597485

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