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A note on the number of primes in short intervals

A note on the number of primes in short intervals

Let <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper J left-parenthesis beta comma upper T right-parenthesis equals integral Subscript 1 Superscript upper T Superscript beta Baseline Baseline left-parenthesis sigma-summation Underscript x greater-than p Superscript k Baseline less-than-or-equal-to x plus x slash upper T Endscripts log p minus x slash upper T right-parenthesis squared …