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.
Soient un corps fini et un polynôme de degré au moins égal à 1. Une fonction sur est dite (complètement) -additive si pour tous tels que . Nous montrons que les vecteurs sont asymptotiquement équirépartis dans l’ensemble image si les sont premiers entre eux deux à deux et si les sont -additives. En outre, nous établissons que les vecteurs sont asymptotiquement indépendants et gaussiens si sont - resp. -additives.
@article{JTNB_2005__17_1_125_0, author = {Drmota, Michael and Gutenbrunner, Georg}, title = {The joint distribution of $Q$-additive functions on polynomials over finite fields}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {125--150}, publisher = {Universit\'e Bordeaux 1}, volume = {17}, number = {1}, year = {2005}, doi = {10.5802/jtnb.481}, zbl = {1129.11040}, mrnumber = {2152215}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jtnb.481/} }
TY - JOUR AU - Drmota, Michael AU - Gutenbrunner, Georg TI - The joint distribution of $Q$-additive functions on polynomials over finite fields JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 125 EP - 150 VL - 17 IS - 1 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.481/ DO - 10.5802/jtnb.481 LA - en ID - JTNB_2005__17_1_125_0 ER -
%0 Journal Article %A Drmota, Michael %A Gutenbrunner, Georg %T The joint distribution of $Q$-additive functions on polynomials over finite fields %J Journal de théorie des nombres de Bordeaux %D 2005 %P 125-150 %V 17 %N 1 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.481/ %R 10.5802/jtnb.481 %G en %F JTNB_2005__17_1_125_0
Drmota, Michael; Gutenbrunner, Georg. The joint distribution of $Q$-additive functions on polynomials over finite fields. Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 1, pp. 125-150. doi : 10.5802/jtnb.481. http://www.numdam.org/articles/10.5802/jtnb.481/
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