Plane curves in boxes and equal sums of two powers
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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.
15 pages; to appear in Math. Zeit
15 pages; to appear in Math. Zeit