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On the second moment for primes in an arithmetic progression

Daniel Goldston·C. Y. Yildirim
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Abstract

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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Daniel Goldston, C. Y. Yildirim. 2000-04-24. On the second moment for primes in an arithmetic progression. https://doi.org/10.4064/aa100-1-8

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