Sökning: "Prime number theorem for arithmetic progressions"

Hittade 2 uppsatser innehållade orden Prime number theorem for arithmetic progressions.

1. 1. An operator theoretic approach to the Riemann Hypothesis

   Master-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten); Lunds universitet/Matematikcentrum

   Författare :Ramon Arjan van de Scheur; [2023]
   Nyckelord :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;

   Sammanfattning : 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. LÄS MER

3. 2. On Special Cases of Dirichlet’s Theorem on Arithmetic Progressions

   Kandidat-uppsats, Lunds universitet/Matematik (naturvetenskapliga fakulteten)

   Författare :Johan Jönsson; [2015]
   Nyckelord :Dirichlet’s Theorem; primes; cyclotomic polynomial; Mathematics and Statistics;

   Sammanfattning : Dirichlet’s theorem regarding existence of infinitely many primes in progressions on the form a, a + n, a + 2n... when (a,n) = 1 is well known and proved by using Dirichlet series. LÄS MER