Residue classes containing an unexpected number of primes Article - Décembre 2012

Daniel Fiorilli

Daniel Fiorilli, « Residue classes containing an unexpected number of primes  », Duke Mathematical Journal, décembre 2012, pp. 2923-2943. ISSN 0012-7094

Abstract

We fix a non-zero integer $a$ and consider arithmetic progressions $a \bmod q$, with $q$ varying over a given range. We show that for certain specific values of $a$, the arithmetic progressions $a \bmod q$ contain, on average, significantly fewer primes than expected.

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