TY - JOUR
T1 - Multiple recurrence and convergence along the primes
AU - Wooley, Trevor D.
AU - Ziegler, Tamar D.
PY - 2012/12
Y1 - 2012/12
N2 - Let E ⊂ ℤ be a set of positive upper density. Suppose that P1,P2,...,Pk ∈ ℤ[X] are polynomials having zero constant terms. We show that the set E ∩ (E -P1(p-1)) ∩ ··· ∩ (E - Pk(p-1)) is non-empty for some prime number p. Furthermore, we prove convergence in L2 of polynomial multiple averages along the primes.
AB - Let E ⊂ ℤ be a set of positive upper density. Suppose that P1,P2,...,Pk ∈ ℤ[X] are polynomials having zero constant terms. We show that the set E ∩ (E -P1(p-1)) ∩ ··· ∩ (E - Pk(p-1)) is non-empty for some prime number p. Furthermore, we prove convergence in L2 of polynomial multiple averages along the primes.
UR - http://www.scopus.com/inward/record.url?scp=84870328104&partnerID=8YFLogxK
U2 - 10.1353/ajm.2012.0048
DO - 10.1353/ajm.2012.0048
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AN - SCOPUS:84870328104
SN - 0002-9327
VL - 134
SP - 1705
EP - 1732
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 6
ER -