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:1-9181 http://hdl.handle.net/20.500.12708/14278 |
Library ID: | AC04223187 | Organisation: | E104 - Institut für Diskrete Mathematik und Geometrie | Publication Type: | Thesis Hochschulschrift |
Appears in Collections: | Thesis |
Files in this item:
File | Description | Size | Format | |
---|---|---|---|---|
The joint distribution of Q-additive functions on polynomials over finite fields.pdf | 2.29 MB | Adobe PDF | ![]() View/Open |
Page view(s)
25
checked on Feb 18, 2021
Download(s)
84
checked on Feb 18, 2021

Google ScholarTM
Check
Items in reposiTUm are protected by copyright, with all rights reserved, unless otherwise indicated.