Polynomial multiple recurrence over rings of integers (Q2828025)
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scientific article; zbMATH DE number 6642624
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Polynomial multiple recurrence over rings of integers |
scientific article; zbMATH DE number 6642624 |
Statements
24 October 2016
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Szemerédi theorem
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polynomial configurations
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van der Waerden theorem
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Polynomial multiple recurrence over rings of integers (English)
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The authors prove a generalization of the polynomial Szemerédi theorem to the case of intersective polynomials over the ring of integers of an algebraic number field, which means polynomials having a common root modulo every ideal. Using an appropriate version of the Furstenberg correspondence principle, this result leads to new examples of the polynomial van der Waerden theorem. The results in the present paper extend earlier results in the field, such as those in [the first author et al., J. Am. Math. Soc. 9, No. 3, 725--753 (1996; Zbl 0870.11015); Adv. Math. 219, No. 1, 369--388 (2008; Zbl 1156.11007)].
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