A note on primes in short intervals

Author: Bazzanella Danilo  

Publisher: Springer Publishing Company

ISSN: 0003-889X

Source: Archiv der Mathematik, Vol.91, Iss.2, 2008-08, pp. : 131-135

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Abstract

This paper is concerned with the number of primes in short intervals. We prove that $$psi(x+x^theta) - psi(x) sim x^theta$$</EquationSource> , for θ</i> > 1/2, with the assumption of an heuristic hypothesis weaker than the Lindelöf hypothesis.