English

On the representation of integers by binary forms

Number Theory 2019-11-13 v2

Abstract

Let FF be a binary form with integer coefficients, non-zero discriminant and degree dd with dd at least 33. Let RF(Z)R_F(Z) denote the number of integers of absolute value at most ZZ which are represented by FF. We prove that there is a positive number CFC_F such that RF(Z)R_F(Z) is asymptotic to CFZ2dC_F Z^{\frac{2}{d}}.

Keywords

Cite

@article{arxiv.1605.03427,
  title  = {On the representation of integers by binary forms},
  author = {C. L. Stewart and Stanley Yao Xiao},
  journal= {arXiv preprint arXiv:1605.03427},
  year   = {2019}
}

Comments

26 pages, revised version

R2 v1 2026-06-22T13:58:27.760Z