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Integer solutions to decomposable form inequalities

โœ Scribed by Zhihua Chen; Min Ru


Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
136 KB
Volume
115
Category
Article
ISSN
0022-314X

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โœฆ Synopsis


This paper obtains a result on the finiteness of the number of integer solutions to decomposable form inequalities. Let k be a number field and let F (X 1 , ..., X m ) be a non-degenerate decomposable form with coefficients in k. We prove that, for every finite set of places S of k containing the archimedean places of k, for each real number < 1 m-1 and for each constant c > 0, the inequality 0 < โˆˆS F (x 1 , ..., x m ) cH S (x 1 , ..., x m ) in (x 1 , ..., x m ) โˆˆ O m S .

(1)

has only finitely many O * S -non-proportional solutions.


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