Polynomial multiple recurrence over rings of integers
2015 ◽
Vol 36
(5)
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pp. 1354-1378
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Keyword(s):
We generalize the polynomial Szemerédi theorem to intersective polynomials over the ring of integers of an algebraic number field, by which we mean polynomials having a common root modulo every ideal. This leads to the existence of new polynomial configurations in positive-density subsets of $\mathbb{Z}^{m}$ and strengthens and extends recent results of Bergelson, Leibman and Lesigne [Intersective polynomials and the polynomial Szemerédi theorem. Adv. Math.219(1) (2008), 369–388] on polynomials over the integers.
1988 ◽
Vol 111
◽
pp. 165-171
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Keyword(s):
1969 ◽
Vol 20
(2)
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pp. 405-405
Keyword(s):
1996 ◽
Vol 119
(2)
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pp. 191-200
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1999 ◽
Vol 42
(1)
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pp. 127-141
Keyword(s):
2018 ◽
Vol 17
(05)
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pp. 1850087
Keyword(s):
1964 ◽
Vol 40
(4)
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pp. 245-246
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Keyword(s):
1971 ◽
Vol 14
(3)
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pp. 405-409
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Keyword(s):
Keyword(s):