Abstract
The best known results about the distribution of prime numbers in short intervals imply that all intervals [n,n+H]⊂[N,2N] contain the expected number of primes for all H≥N7/12, and almost all intervals [n,n+H]⊂[N,2N] contain the expected number of primes for all H≥N1/6. As a natural generalization, this paper is concerned with the distribution of prime numbers in intervals of type [nα,nα+H] with α>1.
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