The joint distribution of q-additive functions

THE JOINT DISTRIBUTION OF q-ADDITIVE FUNCTIONS

q-ADDITIVE FUNCTIONS AND WELL DISTRIBUTION

The Joint Distribution of Q-additive Functions on Polynomials over Finite Fields

Let K be a finite field and Q ∈ K[T ] a polynomial of positive degree. A function f on K[T ] is called (completely) Q-additive if f(A + BQ) = f(A) + f(B), where A,B ∈ K[T ] and deg(A) < deg(Q). We prove that the values (f1(A), ..., fd(A)) are asymptotically equidistributed on the (finite) image set {(f1(A), ..., fd(A)) : A ∈ K[T ]} if Qj are pairwise coprime and fj : K[T ] → K[T ] are Qj-additi...

ON THE JOINT DISTRIBUTION OF q-ADDITIVE FUNCTIONS ON POLYNOMIAL SEQUENCES

The joint distribution of sequences (f`(P`(n)))n∈N, ` = 1, 2, . . . , d and (f`(P`(p)))p∈P respectively, where f` are q`-additive functions and P` polynomials with integer coefficients, is considered. A central limit theorem is proved for a larger class of q` and P` than by Drmota [3]. In particular, the joint limit distribution of the sum-of-digits functions sq1 (n), sq2 (n) is obtained for ar...

Distribution properties of sequences generated by Q-additive functions with respect to Cantor representation of integers

In analogy to ordinary q-additive functions based on q-adic expansions one may use Cantor expansions with a Cantor base Q to define (strongly) Q-additive functions. This paper deals with distribution properties of multi-dimensional sequences which are generated by such Q-additive functions. If in each component we have the same Cantor base Q, then we show that uniform distribution already impli...