ON THE PROBLEM OF INTEGER SOLUTIONS TO DECOMPOSABLE FORM INEQUALITIES
2008 ◽
Vol 04
(05)
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pp. 859-872
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This paper proves a conjecture proposed by Chen and Ru in [1] on the finiteness of the number of integer solutions to decomposable form inequalities. Let k be a number field and let F(X1,…,Xm) be a non-degenerate decomposable form with coefficients in k. We show that for every finite set of places S of k containing the archimedean places of k, for each real number λ < 1 and each constant c > 0, the inequality [Formula: see text] has only finitely many [Formula: see text]-non-proportional solutions, where HS(x1,…,xm) = Πυ∈S max 1≤i≤m ||xi||υ is the S-height.
1983 ◽
Vol 93
(2)
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pp. 219-230
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2012 ◽
Vol 08
(07)
◽
pp. 1569-1580
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