Let P(n) denote the largest prime factor of an integer n >= 2. In this talk, I shall study the equidistribution of the sequence
{f(P(n)) : n >= 1} over the set of congruence classes modulo an integer b >= 2, where f is a strongly q-additive function with integer values (i.e., f(aq^j+b)=f(a)+f(b), with (a,b,j) in N3,
0 <= b < q^j). We also show that, for an irrational number \alpha, the sequence {\alpha P(n) : n >= 1, f(P(n)) \equiv a \mod b} is equidistributed modulo 1, for every a in Z. In addition to that, we estimate some sums involving P(n) under digital constraints
and we finish by proving an asymptotic formula for the cardinality of
the set { n <= x : f(P(n)+c) \equiv a \mod b, P(n) \equiv l mod k}, where c in Z, k >= 2.
Digital functions and the largest prime factor of an integer
16.05.2017 15:15 - 16:45
Organiser:
Ch. Krattenthaler
Location: