Principal forms X^2 + nY^2 representing many integers
Number Theory
2021-02-03 v2
Abstract
In 1966, Shanks and Schmid investigated the asymptotic behavior of the number of positive integers less than or equal to x which are represented by the quadratic form X^2+nY^2. Based on some numerical computations, they observed that the constant occurring in the main term appears to be the largest for n=2. In this paper, we prove that in fact this constant is unbounded as n runs through positive integers with a fixed number of prime divisors.
Cite
@article{arxiv.1003.1094,
title = {Principal forms X^2 + nY^2 representing many integers},
author = {David Brink and Pieter Moree and Robert Osburn},
journal= {arXiv preprint arXiv:1003.1094},
year = {2021}
}
Comments
10 pages, title has been changed, Sections 2 and 3 are new, to appear in Abh. Math. Sem. Univ. Hamburg