A note on Primes in Short Intervals

Mathematics – Number Theory

Scientific paper

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6 pages, report number added

Scientific paper

Instead of a strong quantitative form of the Hardy-Littlewood prime $k$-tuple
conjecture, one can assume an average form of it and still obtains the same
distribution result on $\psi(x+h) - \psi(x)$ by Montgomery and Soundararajan
[1].

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