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Primes in arithmetic progressions to spaced moduli. III

Volume 179 / 2017

Roger Baker Acta Arithmetica 179 (2017), 125-132 MSC: Primary 11N13. DOI: 10.4064/aa8401-5-2017 Published online: 7 July 2017

Abstract

Let \[E(x,q) = \max_{(a,q) = 1} \biggl| \sum_{\substack{n \le x\\ n \equiv a\, ({\rm mod}\, q)}} \Lambda(n) - \frac x{\phi(q)}\biggr|.\] We show that, for $S$ the set of squares, \[\sum_{\substack{q \in S\\ Q \lt q \le 2Q}} E(x, q) \ll_{A,\varepsilon} x Q^{-1/2}(\log x)^{-A} \] for $\varepsilon \gt 0$, $A \gt 0$, and $Q \le x^{1/2-\varepsilon}$. This improves a theorem of the author.

Authors

  • Roger BakerDepartment of Mathematics
    Brigham Young University
    Provo, UT 84602, U.S.A.
    e-mail

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