Primes in arithmetic progressions to spaced moduli. III

Roger Baker¹

¹ Department of Mathematics Brigham Young University Provo, UT 84602, U.S.A.

Acta Arithmetica, Tome 179 (2017) no. 2, pp. 125-132

Résumé

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.

Détail

DOI : 10.4064/aa8401-5-2017

Keywords: max biggl sum substack equiv mod lambda frac phi biggr set squares sum substack varepsilon log a varepsilon varepsilon improves theorem author