On almost-primes in arithmetic progressions (Q5925239)

The author uses the methods of his previous paper [ibid. 13, 387-401 (1989; Zbl 0689.10052)] to obtain the following dual result: For a fixed integer a and \(Q<q\leq 20\), \((q,a)=1\) there exists an almost-prime \(P_ 2\) such that \(P_ 2\equiv a\) mod q, \(P_ 2\leq \tau (a)(\log q)^ 7\) for all except possibly O(Q/log Q) moduli q. Here \(\tau\) denotes the divisor function, and the O-constant is absolute.