Let E subset of Z be a set of positive upper density. Suppose that P-1, P-2, ... , P-k is an element of Z[X] are polynomials having zero constant terms. We show that the set E boolean AND (E - p(1)(p - 1)) boolean AND ... (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.
Bibliographical notePublisher: The Johns Hopkins University Press
- DIFFERENCE SETS
- ERGODIC AVERAGES