Some problems of analytic number theory on arithmetic semigroups

Abstract

Let E be a set of primes with density τ > 0 in the set of primes.Write A for the set of positive integers composed solely of primes from E .We discuss the distribution of the integers from A in short intervals, and whether for fixed k ∈ Z there are solutions to m + k = p with m ∈ A , where p denotes a prime, or m + k = n where n has a large prime factor ( > n ξ for ξ > 1 2 ).

Locations

• Functiones et Approximatio Commentarii Mathematici - View - PDF