# Plane curves in boxes and equal sums of two powers

Research paper by T. D. Browning, D. R. Heath-Brown

Indexed on: 24 Jun '05Published on: 24 Jun '05Published in: Mathematics - Number Theory

#### Abstract

Given an absolutely irreducible ternary form $F$, 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.