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arXiv · 1706.07319

Sparser variance for primes in arithmetic progression

Roger Baker·Tristan Freiberg
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Abstract

We obtain an analog of the Montgomery-Hooley asymptotic formula for the variance of the number of primes in arithmetic progressions. In the present paper the moduli are restricted to the sequences of integer parts $[F(n)]$, where $F(t) = t^c$ ($c > 1$, $c \not\in \mathbb{N}$) or $F(t) = \exp\big((\log t)^{\gamma}\big)$ ($1 < \gamma < 3/2$).

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Roger Baker, Tristan Freiberg. 2017-06-22. Sparser variance for primes in arithmetic progression. https://doi.org/10.1007/s00605-017-1139-6

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