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
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:1-9181
Library ID: AC04223187
Organisation: E104 - Institut für Diskrete Mathematik und Geometrie 
Publication Type: Thesis
Appears in Collections:Thesis

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