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arXiv · 1409.7569

Polynomial multiple recurrence over rings of integers

Vitaly Bergelson·Donald Robertson
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Abstract

We generalize the polynomial Szemer\'{e}di 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 on polynomials over the integers.

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Vitaly Bergelson, Donald Robertson. 2014-09-26. Polynomial multiple recurrence over rings of integers. https://arxiv.org/abs/1409.7569

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