On explicit bounds for the solutions of a class of parametrized Thue equations of arbitrary degree

作     者：Heuberger, C 

作者机构：Graz Tech Univ Math Inst A-8010 Graz Austria 

出 版 物：《MONATSHEFTE FUR MATHEMATIK》 (数学月刊)

年 卷 期：2001年第132卷第4期

页      面：325-339页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Thue equations Diophantine equation linear forms in logarithms 

摘      要：In a recent paper [7] the author considered the family of parametrized Thue equations F-a (X, Y) := Pi (n)(i=1) (X - P-i(a)Y) - Y-n = +/-1, a is an element of N for monic polynomials p(1),...,p(n) is an element of Z[a] which satisfy degp(1) ... degp(n). Under some technical conditions it could be proved that there is a computable constant a(0) = a(0)(p(1),...,P-n) such that for all integers a greater than or equal to a(0) the only integer solutions (x, y) of the Diophantine equation satisfy /y/ less than or equal to 1. In this paper, we give an explicit expression for a(0) depending on the polynomials p(1),...,p(n).