Essays about: "Riemann Hypothesis"

Showing result 1 - 5 of 9 essays containing the words Riemann Hypothesis.

  1. 1. Low-lying zeroes of L-functions attached to modular forms

    University essay from Göteborgs universitet/Institutionen för matematiska vetenskaper

    Author : Alf Söderberg; [2024-03-22]
    Keywords : Number theory; L-functions; Modular forms; Newforms; Low-lying zeros; 1-level density; Density Conjecture; Ratios Conjecture.;

    Abstract : We study the family of L-functions attached to Hecke newforms of weight k and level N and their low-lying zeroes. First, we recall the Density Conjecture of Katz and Sarnak and how it predicts the behaviour of the low-lying zeroes of any natural family of L-functions. 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. 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. 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

  6. 5. 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