Multiple recurrence and convergence for sequences related to the prime numbers
Multiple recurrence and convergence for sequences related to the prime numbers
For any measure preserving system (X,, μ,T) and A ∈ with μ(A) > 0, we show that there exist infinitely many primes p such that (the same holds with p − 1 replaced by p + 1). Furthermore, we show the existence of the limit in L2(μ) of the associated …