English

Plane curves in boxes and equal sums of two powers

Number Theory 2007-05-23 v1

Abstract

Given an absolutely irreducible ternary form FF, the purpose of this paper is to produce better upper bounds for the number of integer solutions to the equation F=0, that are restricted to lie in very lopsided boxes. As an application of the main result, a new paucity estimate is obtained for equal sums of two like powers.

Keywords

Cite

@article{arxiv.math/0506497,
  title  = {Plane curves in boxes and equal sums of two powers},
  author = {T. D. Browning and D. R. Heath-Brown},
  journal= {arXiv preprint arXiv:math/0506497},
  year   = {2007}
}

Comments

15 pages; to appear in Math. Zeit

R2 v1 2026-07-22T17:21:07.350Z