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Thue equations and the method of Coleman-Chabauty | | Dino Lorenzini
; Thomas J. Tucker
; | | Date: |
18 May 2000 | | Subject: | Number Theory MSC-class: 11D41, 14G25, 14G30 | math.NT | | Affiliation: | University of Georgia), Thomas J. Tucker (University of Georgia | | Abstract: | In this paper, we prove that a Thue equation F(x,y) = h, where h is an integer and F is a polynomial of degree n with integer coefficients and without repeated roots, has at most 2n^3 - 2n - 3 solutions provided that the Mordell-Weil rank of the Jacboian of the corresponding curve is less than (n-1)(n-2)/2. The proof uses the method of Coleman-Chabauty, extended here to apply to arbitrary regular models of curves, along with an explicit construction of a portion of a regular model for the curve corresponding to the Thue equation. | | Source: | arXiv, math.NT/0005186 | | Services: | Forum | Review | PDF | Favorites | |
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