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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 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 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 ...

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