ON THE JOINT DISTRIBUTION OF q-ADDITIVE FUNCTIONS ON POLYNOMIAL SEQUENCES
نویسندگان
چکیده
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 arbitrary integers q1, q2. For strongly q-additive functions with respect to the same q, a central limit theorem is proved for arbitrary polynomials P` with the help of a joint representation of the digits of P`(n) by a Markov chain.
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