Essays about: "prime numbers"

Showing result 1 - 5 of 24 essays containing the words prime numbers.

  1. 1. Goldbach’s Conjecture – Numerical Results

    University essay from Mälardalens universitet/Akademin för utbildning, kultur och kommunikation

    Author : Daniel Edqvist; [2023]
    Keywords : Goldbach conjecture; Goldbach partitions; prime numbers; Goldbachs förmodan; Goldbach partitioner; primtal;

    Abstract : The Goldbach conjecture states that every even number greater than 2 can be written as a sumof two prime numbers. This thesis will go through the necessary theory and the backgroundto the problem at hand. READ MORE

  3. 2. The Riemann Hypothesis and the Distribution of Primes

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : David Appelgren; Leo Tikkanen; [2023]
    Keywords : Riemann; Riemann Hypothesis; Zeta Function; Prime Number Theorem;

    Abstract : 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. READ MORE

  4. 3. The Riemann Zeta Function and Prime Numbers

    University essay from KTH/Skolan för teknikvetenskap (SCI)

    Author : Oskar Rune; Linus Envall; [2023]
    Keywords : ;

    Abstract : This thesis is the result of a literature study regarding the relationship between the Riemann zeta function and prime numbers. We introduce the $\zeta$ function, discussing its properties. Then, starting from Riemann's original series, we derive the Euler product formula and functional equation for $\zeta$. READ MORE

  5. 4. An operator theoretic approach to the Riemann Hypothesis

    University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Ramon Arjan van de Scheur; [2023]
    Keywords : Riemann hypothesis; Prime number theorem; Prime number theorem for arithmetic progressions; operator theoretic equivalent; compact operator; prime-counting function; Chebyshev function; Laplace transform; Fourier transform; convolution operator; weak topology; strong topology; compact perturbation; Tauberian theorem; Poisson kernel; holomorphic; self-adjoint; spectrum; trace; Mathematics and Statistics;

    Abstract : 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. READ MORE

  6. 5. The p-adic numbers and Hensel's lemma

    University essay from Lunds universitet/Matematik LTH; Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

    Author : Justyna Dabrowska; [2023]
    Keywords : p-adic; p-adic numbers; number theory; hensel s lemma; Mathematics and Statistics;

    Abstract : The thesis consists of four chapters, each focused on developing the knowledge and drawing new connections with the p-adic numbers and the notions that are well known from the usual analysis on the real topology. In the first chapter, we introduce the basic structure of the $p$-adics, in connection to the conergent series and field axioms. READ MORE