整数环上的多项式多重递归
Polynomial multiple recurrence over rings of integers
摘要：
本文将多项式Szemerédi定理推广到代数数域的整数环上的交多项式，即模每个理想有公共根的多项式。这导致了$\mathbb{Z}^m$的正密度子集中存在新的多项式配置，并加强和扩展了Bergelson、Leibman和Lesigne关于整数上多项式的最新结果。
英文摘要：
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 on polynomials over the integers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
