On the second moment for primes in an arithmetic progression

Details On the second moment for primes in an arithmetic progression On the second moment for primes in an arithmetic progression

2000-04-24

arxiv.org/abs/math/0004149v1

Mathematics

Number Theory

Scientific paper

Assuming the Generalized Riemann Hypothesis, we obtain a lower bound within a constant factor of the conjectured asymptotic result for the second moment for primes in an individual arithmetic progression in short intervals. Previous results were averaged over all progression of a given modulus. The method uses a short divisor sum approximation for the von Mangoldt function, together with some new results for binary correlations of this divisor sum approximation in arithmetic progressions.

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