Multiple recurrence and convergence along the primes

Details Multiple recurrence and convergence along the primes Multiple recurrence and convergence along the primes

2010-01-22

arxiv.org/abs/1001.4081v2

Mathematics

Dynamical Systems

Some changes made in light of comments from the referees

Scientific paper

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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