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The Continuity of the Limiting Distribution of a Function of Two Additive Functions.

Janos Galambos, Imre Kátai (1990)

Mathematische Zeitschrift

The distribution of additive functions defined on short intervals

P.D.T.A. ELLIOTT (1987/1988)

Seminaire de Théorie des Nombres de Bordeaux

The distribution of the sum-of-digits function

Michael Drmota, Johannes Gajdosik (1998)

Journal de théorie des nombres de Bordeaux

By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.

The joint distribution of $Q$ -additive functions on polynomials over finite fields

Michael Drmota, Georg Gutenbrunner (2005)

Journal de Théorie des Nombres de Bordeaux

Let $K$ be a finite field and $Q \in K [T]$ a polynomial of positive degree. A function $f$ on $K [T]$ is called (completely) $Q$ -additive if $f (A + B Q) = f (A) + f (B)$ , where $A, B \in K [T]$ and $deg (A) < deg (Q)$ . We prove that the values $(f_{1} (A), ..., f_{d} (A))$ are asymptotically equidistributed on the (finite) image set ${(f_{1} (A), ...,$ $f_{d} ...$