Plane curves in boxes and equal sums of two powers
T. D. Browning, D. R. Heath-Brown
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.
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