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Plane curves in boxes and equal sums of two powers

T. D. Browning·D. R. Heath-Brown
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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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T. D. Browning, D. R. Heath-Brown. 2005-06-24. Plane curves in boxes and equal sums of two powers. https://arxiv.org/abs/math/0506497

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