Recently, by means of a
new method involving the combinatorial sieve and the bilateral Laplace
transform, we estimated asymptotically the moments of additive functions
f(n) for integers n belonging to certain sets S. From such estimates the
limiting distribution function of these f(n), for n ∈ S, can be determined. Here
the method is applied to the special sequence Sc= {p + c}, where p runs
through all the primes and c is an arbitrary fixed integer. Various distribution
properties of the sequence Sc, such as those given by the Brun-Titchmarch
inequality and Bombieri’s theorem, are used. Previously Barban had established
distribution results for certain f(n) when n ∈ Sc, but it was not known (until now)
under what conditions the moments could be asymptotically estimated as
well.
