Praštevilski izrek

delo diplomskega seminarja

Andraž Maier (Author), Barbara Drinovec-Drnovšek (Mentor)

Abstract

V delu z analitičnimi metodami dokažemo praštevilski izrek. V ta namen predstavimo osnovno teorijo neskončnih produktov in vpeljemo Riemannovo funkcijo zeta. Izpeljemo Eulerjevo produktno formulo, poiščemo meromorfno razširitev funkcije zeta na desno polovico kompleksne ravnine in predpis za njen logaritmični odvod. Definiramo Mangoldtovo funkcijo in funkcijo psi ter z njuno pomočjo poiščemo ekvivalentno obliko praštevilskega izreka, ki ga nazadnje dokažemo z metodami kompleksne analize.

Keywords

matematika;praštevilski izrek;Riemannova funkcija zeta;

Data

Language:	Slovenian
Year of publishing:	2021
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[A. Maier]
UDC:	511
COBISS:	77668611
Views:	804
Downloads:	105
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Prime number theorem
Secondary abstract:	In this work, prime number theorem is proven using analytic methods. For this purpose elementary theory of infinite products is introduced and the Riemann zeta function is used. We derive the Euler product formula and find a meromorphic extension of the zeta function to the right half of the complex plane and the expression for its logarithmic derivative. We also define the Mangoldt and psi function and use them to find an equivalent formulation of the prime number theorem. Finally, the prime number theorem is proved using complex analytic methods.
Secondary keywords:	mathematics;prime number theorem;Riemann zeta function;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	33 str.
ID:	13505876