On the distribution of integers with a fixed number of prime factors.
In finite Galois extensions of with pairwise coprime discriminants the integral and the prime divisors subject to the condition are equidistributed in the sense of E. Hecke.
A natural number is said to be a -integer if , where and is not divisible by the th power of any prime. We study the distribution of such -integers in the Piatetski-Shapiro sequence with . As a corollary, we also obtain similar results for semi--free integers.
In this paper, we give a new upper-bound for the discrepancyfor the sequence , when and .