Koreni multiplikativnih funkcij

diplomsko delo

Mateja Vojsk (Author), Daniel Eremita (Mentor)

Abstract

V diplomskem delu so predstavljene osnove teorije aritmetičnih funkcij. Obravnavane so multiplikativne funkcije na splošno in tudi določeni primeri, kot sta Möbiusova in Eulerjeva funkcija. V prvem delu sta obravnavana Dirichletov produkt in Dirichletov inverz aritmetične funkcije. V drugem delu so formalne potenčne vrste obravnavane algebraično kot elementi kolobarja formalnih potenčnih vrst. Osrednji del diplomskega dela je namenjen korenom multiplikativnih funkcij. Zapisane in dokazane so eksplicitne formule n korenov popolnoma multiplikativnih in kvadratnih aritmetičnih funkcij ter inverzov teh funkcij.

Keywords

diplomska dela;matematika;aritmetične funkcije;kvadratni koreni;racionalni koreni;

Data

Language:	Slovenian
Year of publishing:	2012
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[M. Vojsk]
UDC:	51(043.2)
COBISS:	19484936
Views:	1195
Downloads:	99
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	ROOTS OF MULTIPLICATIVE FUNCTIONS
Secondary abstract:	In the first part of the graduation thesis the basics of the theory of aritmetic functions are presented. We consider multiplicative functions in general as well as specific cases, such as the Möbius function and Euler Phi-function. In this chapter we also consider Dirichlet convolution and Dirichlet inverse of arithmetic function. In the second chapter, we consider formal power series algebraically as elements of the ring of formal power series. The central part of the thesis is devoted to roots of multiplicative functions. We derive explicit formulas of n roots of completely multiplicative and quadratic arithmetic functions as well inverses of these functions.
Secondary keywords:	arithmetic function;multiplicative function;completely multiplicative function;Dirichlet convolution;formal power series;square roots;rational roots;
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:	1001650