Bombieri-Vinogradov Type Theorem for Sparse Sets of Moduli

Stephan Baier, Liangyi Zhao

Published 2006-02-07, updated 2006-10-09Version 4

In this paper, we establish theorems of Bombieri-Vinogradov type and Barban-Davenport-Halberstam type for sparse sets of moduli. As an application, we prove that there exist infinitely many primes of the form $p=am^2+1$ such that $a\leq p^{5/9+\epsilon}$.