Sökning: "prime-counting function"
Hittade 4 uppsatser innehållade orden prime-counting function.
1. The Riemann Hypothesis and the Distribution of Primes
Kandidat-uppsats, KTH/Skolan för teknikvetenskap (SCI)Sammanfattning : The aim of this thesis is to examine the connection between the Riemannhypothesis and the distribution of prime numbers. We first derive theanalytic continuation of the zeta function and prove some of its propertiesusing a functional equation. LÄS MER
2. An operator theoretic approach to the Riemann Hypothesis
Master-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/MatematikcentrumSammanfattning : In 2023 an operator theoretic approach to the Prime Number Theorem was introduced by Olsen. In this thesis this approach is examined and applied to give a new, operator theoretic, proof of a different version of the Prime Number Theorem and of the Prime Number Theorem for arithmetic progressions. LÄS MER
3. Riemann's Zeta Function and Prime Numbers : an approximation using von Mangoldt's explicit formula
Kandidat-uppsats, Umeå universitet/Institutionen för matematik och matematisk statistikSammanfattning : This essay aims to explain the connection between Riemann's zeta function and prime numbers. It relies heavily on Riemann's 1859 manuscript, in which he approximates the prime-counting function using the non-trivial zeros of the zeta function. LÄS MER
4. The Dirichlet Series To The Riemann Hypothesis
Kandidat-uppsats, Högskolan i Gävle/Avdelningen för elektronik, matematik och naturvetenskapSammanfattning : This paper examines the Riemann zeta-function and its relation to the prime distribution. In this work, I present the journey from the Dirichlet series to the Riemann hypothesis. Furthermore, I discuss the prime counting function, the Riemann prime counting function and the Riemann explicit function for distribution of primes. LÄS MER