Density of solutions to quadratic congruences
Number Theory
2016-05-03 v1
Abstract
A classical result in number theory is Dirichlet's theorem on the density of primes in an arithmetic progression. We prove a similar result for numbers with exactly k prime factors for k>1. Building upon a proof by E.M. Wright in 1954, we compute the natural density of such numbers where each prime satisfies a congruence condition. As an application, we obtain the density of squarefree n not greater than x with k prime factors such that a fixed quadratic equation has exactly 2^k solutions modulo n.
Keywords
Cite
@article{arxiv.1605.00088,
title = {Density of solutions to quadratic congruences},
author = {Neha Prabhu},
journal= {arXiv preprint arXiv:1605.00088},
year = {2016}
}