MULTIPLE RECURRENCE AND CONVERGENCE ALONG THE PRIMES

作者：Wooley Trevor D^*; Ziegler Tamar D

来源：American Journal of Mathematics, 2012, 134(6): 1705-1732.

DOI：10.1353/ajm.2012.0048

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.

• 出版日期2012-12