The variance of the number of prime polynomials in short intervals and in residue classes
classification
🧮 math.NT
keywords
intervalsnumbershortvariancearithmeticclassesconcerningconjectures
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We resolve a function field version of two conjectures concerning the variance of the number of primes in short intervals (Goldston and Montgomery) and in arithmetic progressions (Hooley). A crucial ingredient in our work are recent equidistribution results of N. Katz.
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