arxiv: 1001.4081 · v2 · pith:RQCPLFCUnew · submitted 2010-01-22 · 🧮 math.DS · math.NT

Multiple recurrence and convergence along the primes

Trevor D. Wooley , Tamar D. Ziegler This is my paper

classification 🧮 math.DS math.NT

keywords alongconvergencemathbbmultipleprimesaveragesconstantdensity

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Let $E\subset \mathbb Z$ be a set of positive upper density. Suppose that $P_1,P_2,..., P_k\in \mathbb Z[X]$ are polynomials having zero constant terms. We show that the set $E\cap (E-P_1(p-1))\cap ... \cap (E-P_k(p-1))$ is non-empty for some prime number $p$. Furthermore, we prove convergence in $L^2$ of polynomial multiple averages along the primes.

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Multiple recurrence and convergence along the primes

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