--- _id: '214' abstract: - lang: eng text: 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: - first_name: Timothy D full_name: Timothy Browning id: 35827D50-F248-11E8-B48F-1D18A9856A87 last_name: Browning orcid: 0000-0002-8314-0177 - first_name: Roger full_name: Heath-Brown, Roger last_name: Heath Brown citation: ama: Browning TD, Heath Brown R. Plane curves in boxes and equal sums of two powers. Mathematische Zeitschrift. 2005;251(2):233-247. doi:10.1007/s00209-004-0719-z apa: Browning, T. D., & Heath Brown, R. (2005). Plane curves in boxes and equal sums of two powers. Mathematische Zeitschrift. Unknown. https://doi.org/10.1007/s00209-004-0719-z chicago: Browning, Timothy D, and Roger Heath Brown. “Plane Curves in Boxes and Equal Sums of Two Powers.” Mathematische Zeitschrift. Unknown, 2005. https://doi.org/10.1007/s00209-004-0719-z. ieee: T. D. Browning and R. Heath Brown, “Plane curves in boxes and equal sums of two powers,” Mathematische Zeitschrift, vol. 251, no. 2. Unknown, pp. 233–247, 2005. ista: Browning TD, Heath Brown R. 2005. Plane curves in boxes and equal sums of two powers. Mathematische Zeitschrift. 251(2), 233–247. mla: Browning, Timothy D., and Roger Heath Brown. “Plane Curves in Boxes and Equal Sums of Two Powers.” Mathematische Zeitschrift, vol. 251, no. 2, Unknown, 2005, pp. 233–47, doi:10.1007/s00209-004-0719-z. short: T.D. Browning, R. Heath Brown, Mathematische Zeitschrift 251 (2005) 233–247. date_created: 2018-12-11T11:45:15Z date_published: 2005-09-01T00:00:00Z date_updated: 2021-01-12T06:55:33Z day: '01' doi: 10.1007/s00209-004-0719-z extern: 1 intvolume: ' 251' issue: '2' main_file_link: - open_access: '1' url: https://arxiv.org/abs/math/0506497 month: '09' oa: 1 page: 233 - 247 publication: Mathematische Zeitschrift publication_status: published publisher: Unknown publist_id: '7699' quality_controlled: 0 status: public title: Plane curves in boxes and equal sums of two powers type: journal_article volume: 251 year: '2005' ...