Essays about: "Prime number theorem for arithmetic progressions"

Found 2 essays containing the words Prime number theorem for arithmetic progressions.

1. 1. 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

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

   University essay from Lunds universitet/Matematik (naturvetenskapliga fakulteten)

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

   Abstract : 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. READ MORE