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PRIME NUMBERS IN INTERVALS STARTING AT A FIXED POWER OF THE INTEGERS

Published online by Cambridge University Press:  01 August 2009

DANILO BAZZANELLA
DANILO BAZZANELLA*
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, 10129 Torino, Italy (email: [email protected])
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Abstract

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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.

Keywords

prime numbers in short intervals
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 87 , Issue 1 , August 2009 , pp. 83 - 99
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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