Lemma 2.3. Assuming that:

  • z3

  • g:[0,1] multiplicative

  • for some K,A we have

    pzg(p) log pκ log z+A.

Then
1mzh(m)2pz1(eκ+1)(1g(p)),

where h is defined in terms of g as in Selberg’s sieve.