The Bateman-Horn Conjecture: Heuristics, History, and Applications
Number Theory
2021-02-05 v4 History and Overview
Abstract
The Bateman-Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green-Tao theorem, along with many famous conjectures, such the twin prime conjecture and Landau's conjecture. We discuss the Bateman-Horn conjecture, its applications, and its origins.
Keywords
Cite
@article{arxiv.1807.08899,
title = {The Bateman-Horn Conjecture: Heuristics, History, and Applications},
author = {Soren Laing Aletheia-Zomlefer and Lenny Fukshansky and Stephan Ramon Garcia},
journal= {arXiv preprint arXiv:1807.08899},
year = {2021}
}
Comments
47 pages, formerly titled "One conjecture to rule them all: Bateman-Horn," to appear in Expositiones Mathematicae