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The variance of the number of prime polynomials in short intervals and in residue classes
variance the number of prime polynomials short intervals residue classes Number Theory
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2012/4/23
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 i...
Residue classes containing an unexpected number of primes
Residue classes unexpected number of primes
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2010/12/6
We fix a non-zero integer a and consider arithmetic progressions a mod q, with q varying over a given range. We show that for certain specific values of a, the arithmetic progressions a mod q contain,...