Polynomial multiple recurrence over rings of integers
Bergelson, Vitaly · Robertson, Donald
Original · EN
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 Zᵐ and strengthens and extends recent results of Bergelson, Leibman and Lesigne on polynomials over the integers.
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