Plane curves in boxes and equal sums of two powers

Details Plane curves in boxes and equal sums of two powers Plane curves in boxes and equal sums of two powers

2005-06-24

arxiv.org/abs/math/0506497v1

Mathematics

Number Theory

15 pages; to appear in Math. Zeit

Scientific paper

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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