Essays about: "Prime number theorem"

Showing result 1 - 5 of 11 essays containing the words Prime number theorem.

  1. 1. 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

  3. 2. 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

  4. 3. 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

  5. 4. On The Prime Number Theorem

    University essay from Uppsala universitet/Analys och sannolikhetsteori

    Author : Yacoub Hendi; [2021]
    Keywords : ;

    Abstract : .... READ MORE

  6. 5. The Implementation of the Frequency-Time Encoded Decoy-State Protocol with the Slow-Light Effect for Quantum Memories

    University essay from Lunds universitet/Fysiska institutionen; Lunds universitet/Atomfysik

    Author : Koray Dinçer; [2017]
    Keywords : QKD; Decoy-State; Frequency-Time; Slow-light; Quantum Repeater; Quantum Memory; Physics and Astronomy;

    Abstract : Quantum key distribution (QKD) is a secure encryption key generation process to be used by two users in the presence of an eavesdropper. The no-cloning theorem allows the sender "Alice" to securely send qubits with single photons to the receiver "Bob". READ MORE