On a generalization of the Selberg formula

✍ Scribed by Emmanuel Knafo

• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 220 KB
• Volume: 125
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.10.013

✦ Synopsis

In this paper, we prove a theorem related to the asymptotic formula for ψ k (x; q, a) which is used to count numbers up to x with at most k distinct prime factors (or k-almost primes) in a given arithmetic progression a (mod q). This theorem not only gives the asymptotic formula for ψ k (x; q, a) (or Selberg formula), but has played an essential role, recently, in obtaining a lower bound for the variance of distribution of almost primes in arithmetic progressions.