The joint distribution of -additive functions on polynomials over finite fields
Michael Drmota, Georg Gutenbrunner (2005)
Journal de Théorie des Nombres de Bordeaux
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Let be a finite field and a polynomial of positive degree. A function on is called (completely) -additive if , where and . We prove that the values are asymptotically equidistributed on the (finite) image set if are pairwise coprime and are -additive. Furthermore, it is shown that are asymptotically independent and Gaussian if are - resp. -additive.