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Title:
Neke karakterizacije racionalnih aritmetičkih funkcija stupnja (1,1)
Authors:
ID
Vasiljević, Nani
(Author)
ID
Eremita, Daniel
(Mentor)
More about this mentor...
Files:
MAG_Vasiljevic_Nani_2019.pdf
(1,13 MB)
MD5: 1197600056C930170D6618761C3EA35F
PID:
20.500.12556/dkum/7f6123bd-8c65-49c2-9f26-a64e19daabc1
Language:
Croatian
Work type:
Master's thesis/paper
Typology:
2.09 - Master's Thesis
Organization:
FNM - Faculty of Natural Sciences and Mathematics
Abstract:
Dirichletov produkt potpuno multiplikativne funkcije i inverza potpuno multiplikativne funkcije definiramo kao racionalnu aritmetičku funkciju stupnja (1,1). U ovom diplomskom radu, koji se sastoji od tri poglavlja, u prvom dijelu donosimo osnovnu teoriju aritmetičkih funkcija, točnije navodimo definicije i svojstva nekih multiplikativnih funkcija. U drugom dijelu prvo definiramo Dirichletov produkt (konvoluciju) aritmetičkih funkcija i Dirichletov inverz aritmetičke funkcije, zatim slijede iskazi i dokazi nekih karakterizacija potpuno multiplikativnih funkcija. Konačno, u trećem poglavlju definiramoracionalne aritmetičke funkcije stupnja (1,1). Jedan od najpoznatijih primjera je Eulerova funkcija. U literaturi postoji veliki broj karakterizacija potpuno multiplikativnih funkcija, dok karakterizacije racionalnih aritmetičkih funkcija stupnja (1,1) nisu često proučavane, stoga iznosimo neke njihove karakterizacije koje su dostupne u navedoj literaturi.
Keywords:
aritmetička funkcija
,
multiplikativna funkcija
,
potpuno multiplikativna funkcija
,
Eulerova funkcija
,
Dirichletov produkt (kovolucija) aritmetičkih funkcija
,
racionalna aritmetička funkcija stupnja (1
,
1)
Place of publishing:
Maribor
Publisher:
[N. Vasiljević]
Year of publishing:
2019
PID:
20.500.12556/DKUM-74799
UDC:
511.1(043.2)
COBISS.SI-ID:
24932104
NUK URN:
URN:SI:UM:DK:TZBHV4RG
Publication date in DKUM:
22.11.2019
Views:
1098
Downloads:
72
Metadata:
Categories:
FNM
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:
VASILJEVIĆ, Nani, 2019,
Neke karakterizacije racionalnih aritmetičkih funkcija stupnja (1,1)
[online]. Master’s thesis. Maribor : N. Vasiljević. [Accessed 9 April 2025]. Retrieved from: https://dk.um.si/IzpisGradiva.php?lang=eng&id=74799
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Licences
License:
CC BY-NC-ND 4.0, Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International
Link:
http://creativecommons.org/licenses/by-nc-nd/4.0/
Description:
The most restrictive Creative Commons license. This only allows people to download and share the work for no commercial gain and for no other purposes.
Licensing start date:
06.09.2019
Secondary language
Language:
English
Title:
Some characterizations of rational arithmetic functions of degree (1,1)
Abstract:
The Dirichlet product (convolution) of a completely multiplicative function and the inverse of a completely multiplicative function is defined as rational arithmetical function of degree (1,1). In the first part of this master thesis, which consists of three chapters, we provide basic theory of arithmetic functions. Namely, we provide definitions and some properties of few multiplicative functions. In the second part, we provide definition and propertiesrelated to Dirichlet inverse of arithmetic function and Dirichlet convolution of arithmetic functions. Finally, in the last chapter we bring definition for rational arithmetical functions of degree (1,1). Euler's phi- function is a well known example. In the literature there is a large number of characterizations of completely multiplicative functions, comparing to characterizations of totients (rational arithmetical functions of degree (1,1)) , so here we present some further characterizations.
Keywords:
arithmetic function
,
multiplicative function
,
completely multiplicative function
,
Euler's phi-function
,
Dirichlet convolution
,
totient function
,
rational arithmetical function of degree (1
,
1)
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