Grupe aritmetičnih funkcij

diplomsko delo

Mateja Žnidarič (Author), Daniel Eremita (Mentor)

Abstract

V diplomskem delu je predstavljena teorija aritmetičnih funkcij s poudarkom na multiplikativnih in anti multiplikativnih funkcijah. Podrobno je obravnavana grupa aritmetičnih funkcij, ki jo poraja Dirichletov produkt. Opisana je struktura te grupe. Prav tako je podrobno obravnavana podgrupa vseh aritmetičnih funkcij, ki število 1 preslikajo v 1. Ta podgrupa je obravnavana tudi kot vektorski prostor nad poljem racionalnih števil. EricTemple Bell je posebne potenčne vrste, ki jim pravimo Bellove vrste, uporabil za študij lastnosti multiplikativnih aritmetičnih funkcij. V diplomskem delu poiščemo Bellove vrste nekaterih multiplikativnih funkcij. Z Bellovimi vrstami so izpeljani nekateri rezultati, povezani z linearno neodvisnostjo multiplikativnih funkcij.

Keywords

matematika;aritmetika;funkcije;grupe;Bellove vrste;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Žnidarič]
UDC:	51(043.2)
COBISS:	18607624
Views:	1659
Downloads:	126
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	GROUPS OF ARITHMETICAL FUNCTION
Secondary abstract:	This graduation thesis presents the theory of arithmetical functions with emphasis on multiplicative and antimultiplicative functions. The group of arithmetical functions according to the Dirichlet product is considered. The structure of this group is also described. The subgroup of all arithmetical functions which map 1 to 1 is also considered. We consider this subgroup as a vector space over the field of rational numbers. Eric Temple Bell had used special power series for studying properties of multiplicative arithmetical function. His special power series are now called Bell series. Bell series of some multiplicative functions are determinated. Using Bell series some results on linear independence of multiplicative function are obtained.
Secondary keywords:	Arithmetical functions;Dirichlet product;multiplicative functions;antimultiplicative functions;group of arithmatical functions;Bell series.;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	48 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19479