Title: The joint distribution of Q-additive functions on polynomials over finite fields Language: English Authors: Gutenbrunner, Georg Qualification level: Doctoral Advisor: Drmota, Michael Assisting Advisor: Grabner, Peter Issue Date: 2004 Number of Pages: 71 Qualification level: Doctoral Abstract: 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 $f(A+BQ)=f(A)+f(B)$, where $A,B\in K[T]$ and $\deg(A)<\deg(Q)$.We prove that the values $(f_1(A),\ldots,f_d(A))$ are asymptotically equidistributed on the (finite) image set $\{(f_1(A),\ldots,f_d(A)) :A\in K[T]\}$ if $Q_j$ are pairwise coprime and $f_j : K[T] o K[T]$ are $Q_j$-additive. Furthermore, it is shown that $(g_1(A),g_2(A))$ are asymptotically independent and Gaussian if $g_1,g_2: K[T] o \R$ are $Q_1$- resp. $Q_2$-additive. URI: https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-9181http://hdl.handle.net/20.500.12708/14278 Library ID: AC04223187 Organisation: E104 - Institut für Diskrete Mathematik und Geometrie Publication Type: ThesisHochschulschrift Appears in Collections: Thesis

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