PIATETSKI-SHAPIRO PRIMES IN THE INTERSECTION OF MULTIPLE BEATTY SEQUENCES

Suppose that alpha(1), alpha(2), ss(1), ss(2). R. Let alpha(1), alpha(2) > 1 be irrational and of finite type such that 1, a-1 1, a -1 2 are linearly independent over Q. Let c be a real number in the range 1 < c < 12/11. In this paper, it is proved that there exist infinitely many primes in the intersection of the Beatty sequences B-a1,(ss 1) =(sic)alpha(1)n + ss(1)(sic) B-alpha 2,(ss 2) =(sic)a(2)n + ss(2)(sic) and the Piatetski-Shapiro sequence N(c) =.nc.. Moreover, we also give a sketch of the proof of Piatetski-Shapiro primes in the intersection of multiple Beatty sequences.