Essays about: "Zeta Function"

Showing result 1 - 5 of 9 essays containing the words Zeta Function.

  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. Riemann's Zeta Function and Prime Numbers : an approximation using von Mangoldt's explicit formula

    University essay from Umeå universitet/Institutionen för matematik och matematisk statistik

    Author : Jesper Jakobsson; [2023]
    Keywords : complex analysis; prime numbers; prime-counting function; zeta function; Riemann hypothesis; von Mangoldt s explicit formula;

    Abstract : 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. READ MORE

  5. 4. The Dirichlet Series To The Riemann Hypothesis

    University essay from Högskolan i Gävle/Avdelningen för elektronik, matematik och naturvetenskap

    Author : Daud Nawaz; [2018]
    Keywords : ;

    Abstract : 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. READ MORE

  6. 5. An Introduction to Dirichlet Series

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

    Author : Eda Dagasan; [2018]
    Keywords : Mathematics; Dirichlet Series; Riemann Zeta Function; Complex Analysis; Bohr s Theorem; Mathematics and Statistics;

    Abstract : We establish the central convergence properties of ordinary Dirichlet series, including the classical result by Bohr, providing uniform convergence of the series where it has a bounded analytic continuation. We also derive a lower bound for the supremum of Dirichlet polynomials using Kronecker's theorem, of which we see one proof. READ MORE