@article{214, 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.}, author = {Timothy Browning and Heath-Brown, Roger}, journal = {Mathematische Zeitschrift}, number = {2}, pages = {233 -- 247}, publisher = {Unknown}, title = {{Plane curves in boxes and equal sums of two powers}}, doi = {10.1007/s00209-004-0719-z}, volume = {251}, year = {2005}, }