Advanced search

Showing result 1 - 5 of 25 essays matching the above criteria.

  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. Längtande Kroppar: Höga Visan som Pedagogik för Begären

    University essay from Göteborgs universitet/Institutionen för litteratur, idéhistoria och religion

    Author : Nivea Schnizler; [2022-06-22]
    Keywords : Song of Songs; desire; eros; sexuality; common life; Höga Visan; begär; längtan; sexualitet; gemensamt liv;

    Abstract : This study explores how the Song of Songs could and should be interpreted in its own form, i.e., as erotic poetry, and on the basis of sexual desire. READ MORE

  5. 4. A Prime or Not a Prime? That is the Question

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

    Author : Vetle Tjora; [2022]
    Keywords : primality testing; Lucas--Lehmer; number theory; cubic reciprocity; Mersenne primes; Mathematics and Statistics;

    Abstract : In this survey, we shall prove the Lucas–Lehmer primality test used to find the Mersenne primes. A proof of the Law of Cubic Reciprocity will also be presented, which will be applied in the proof of a generalisation of the Lucas–Lehmer primality test... READ MORE

  6. 5. Cyclotomic Fields and Fermat's Last Theorem

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

    Author : Samuel Runyeon Odeberg; [2021]
    Keywords : pure mathematics; number theory; algebra; algebraic number theory; cyclotomic fields; cyclotomic rings; cycltomic integers; Fermat s last theorem; Mathematics and Statistics;

    Abstract : Number theory is in a sense among the oldest disciplines of mathematics. A running theme is that many number theoretic problems are very easy to state and understand. However, actually solving these problems often requires much work or some very clever trick. READ MORE