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<div class="csl-entry">Gutenbrunner, G. (2004). <i>The joint distribution of Q-additive functions on polynomials over finite fields</i> [Dissertation, Technische Universität Wien]. reposiTUm. https://resolver.obvsg.at/urn:nbn:at:at-ubtuw:1-9181</div>
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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 $\deg(A)<\deg(Q)$.<br />We prove that the values $(f_1(A),\ldots,f_d(A))$ are asymptotically equidistributed on the (finite) image set $\{(f_1(A),\ldots,f_d(A)) :<br />A\in K[T]\}$ 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.
de
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Additive Funktion
de
dc.subject
Verallgemeinerung
de
dc.subject
Polynomring
de
dc.subject
Galois-Feld
de
dc.subject
Wahrscheinlichkeitsverteilung
de
dc.title
The joint distribution of Q-additive functions on polynomials over finite fields
en
dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Georg Gutenbrunner
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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dc.contributor.assistant
Grabner, Peter
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tuw.publication.orgunit
E104 - Institut für Diskrete Mathematik und Geometrie