Almost all short intervals containing prime numbers
نویسندگان
چکیده
منابع مشابه
Primes in Almost All Short Intervals
It is well known that Huxley’s density estimates [5] for the zeros of the Riemann zeta-function yield J(x, h) = o(xh2(log x)−2), but only for h ≥ x1/6(log x) , for some C > 0. The weaker result with h ≥ x1/6+ε is proved in Saffari and Vaughan [8], Lemma 5, and in [13], where an identity of Heath-Brown (Lemma 1 of [3]) is used. This paper is inspired by Heath-Brown’s extension [4] of Huxley’s Th...
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I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I authorize the University of Waterloo to lend this thesis to other institutions or individuals for the purpose of scholary research and I understand that my thesis may be made electonically available to the public. iii This thesis is...
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Let X be a large parameter. We will first give a new estimate for the integral moments of primes in short intervals of the type (p, p+ h], where p ≤ X is a prime number and h = o(X). Then we will apply this to prove that for every λ > 1/2 there exists a positive proportion of primes p ≤ X such that the interval (p, p+λ logX] contains at least a prime number. As a consequence we improve Cheer an...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1996
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-76-1-21-84