diplomsko delo
Nataša Geršak (Author), Daniel Eremita (Mentor)

Abstract

Diplomsko delo obravnava aritmetične funkcije in posebno skupino teh funkcij, periodične aritmetične funkcije. V prvem poglavju je vpeljana definicija aritmetičnih funkcij. Obravnavane so pomembnejše aritmetične funkcije in njihove lastnosti. Predstavljene so multiplikativne funkcije in Dirichletov produkt. Izpeljana je tudi Möbiusova formula inverzije. V naslednjem poglavju so definirane kongruence, karakterji končnih Abelovih grup in Dirichletovi karakterji. V zadnjem poglavju so predstavljene periodične aritmetične funkcije, Ramanujanova vsota, posplošitve te vsote in posebni primeri. Obravnavana je tudi Gaussova vsota.

Keywords

matematika;aritmetične funkcije;Gaussova vsota;multiplikativne funkcije;periodične funkcije;diplomska dela;

Data

Language: Slovenian
Year of publishing:
Source: Maribor
Typology: 2.11 - Undergraduate Thesis
Organization: UM FNM - Faculty of Natural Sciences and Mathematics
Publisher: [N. Geršak]
UDC: 51(043.2)
COBISS: 17480968 Link will open in a new window
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Downloads: 164
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Other data

Secondary language: English
Secondary title: PERIODIC ARITHMETICAL FUNCTIONS
Secondary abstract: In this graduation thesis a periodic arithmetical functions and their properties are studied. In the first chapter basic theory of the arithmetical functions is developed. Several examples of the arithmetical functions are given. Also multiplicative functions and the Dirichlet multiplication are presented. Furthermore, the Möbius inversion formula is derived. In the next chapter congruences, characters of finite abelian groups and Dirichlet character are defined. In the last chapter periodic arithmetical functions, Ramanujan's sum, its generalizations and special cases are presented. Also a Gauss sum is considered.
Secondary keywords: arithmetical function;Dirichlet character;Gauss sum;multiplicative function;periodic arithmetical function;Ramanujan's sum;
URN: URN:SI:UM:
Type (COBISS): Undergraduate thesis
Thesis comment: Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages: VIII, 57 f.
Keywords (UDC): mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID: 18368
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