Bombieri-Vinogradov Type Theorem for Sparse Sets of Moduli

Abstract

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 $p=a{m}^2+1$ such that $a\le p^{5/9+\hat{I}\mu }$.

11 Pages