paper

Plane curves in boxes and equal sums of two powers

arXiv:math/0506497

Abstract

Given an absolutely irreducible ternary form , 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.

15 pages; to appear in Math. Zeit

Plane curves in boxes and equal sums of two powers · wovepaper