Essays about: "Riemann"

Showing result 1 - 5 of 41 essays containing the word Riemann.

  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. Supersymmetry in Quantum Mechanics

    University essay from Uppsala universitet/Institutionen för materialvetenskap

    Author : Ludvig Chen; [2023]
    Keywords : Quantum Mechanics; Supersymmetry; Witten Index; Morse Theory;

    Abstract : The introduction of supersymmetry has led to great progress in the study of quantum field theories. Notably, with supersymmetry, properties of a quantum field theory can be computed with higher precision than what would otherwise be possible. In this project, we investigate supersymmetry in the context of quantum mechanics. READ MORE

  4. 3. 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

  5. 4. 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

  6. 5. Elementary proof of the Riemann—Roch Theorem

    University essay from Uppsala universitet/Algebra, logik och representationsteori

    Author : Hampus Sundgren; [2023]
    Keywords : Algebraic Geometry; Riemann–Roch; The Riemann–Roch Theorem; Divisors; Differentials; L D ; l D ; Vector space L D ; Proof of the Riemann–Roch Theorem;

    Abstract : This thesis will cover an elementary proof of the Riemann–Roch Theorem for planecurves. We will introduce the notions of divisors, which is a convenient way of com-puting multiplicities of rational function, then continuing by introducing differentials. READ MORE