Distribution propertiesof digital expansionsarising from linear recurrences

In: Mathematica Slovaca, vol. 53, no. 1

Mario Lamberger - Jörg M. Thuswaldner

Detaily:

Rok, strany: 2003, 1 - 20

O článku:

Let $(G_j)_j≥0$ be a strictly increasing sequence of non-negative integers defined by a linear recurrence relation. Let $S_G(n)$ denote the $G$@-ary sum-of-digits function. In this paper we establish several distribution results for $S_G(n)$ which include an analogue of a result of A. O. Gel'fond on the distribution of the $q$@-ary sum-of-digits function in residue classes as well as an Erd\H os-Kac-type theorem. The main tool in the proofs of these results is an estimate for exponential sums of the form

$$ | ∑_n<N \exp (2π i ((( $r$ ) / ( $s$ )) S_G(n)+yn))| \ll N^λ , $$

where $r,s \in \Bbb Z$, $y\in\Bbb R$ and $λ<1$.

Ako citovať:

ISO 690:

Lamberger, M., Thuswaldner, J. 2003. Distribution propertiesof digital expansionsarising from linear recurrences. In Mathematica Slovaca, vol. 53, no.1, pp. 1-20. 0139-9918.

APA:

Lamberger, M., Thuswaldner, J. (2003). Distribution propertiesof digital expansionsarising from linear recurrences. Mathematica Slovaca, 53(1), 1-20. 0139-9918.