diplomsko delo
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: |
2010 |
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
|
Views: |
2174 |
Downloads: |
164 |
Average score: |
0 (0 votes) |
Metadata: |
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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 |