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Inequalities for Decomposable Forms of Degree n + 1 in n Variables

Jeffrey Lin Thunder
Transactions of the American Mathematical Society
Vol. 354, No. 10 (Oct., 2002), pp. 3855-3868
Stable URL: http://www.jstor.org/stable/3072986
Page Count: 14
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Inequalities for Decomposable Forms of Degree n + 1 in n Variables
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Abstract

We consider the number of integral solutions to the inequality ∣ F( x)∣ ≤ m, where F( X)∈ Z[ X] is a decomposable form of degree n + 1 in n variables. We show that the number of such solutions is finite for all m only if the discriminant of F is not zero. We get estimates for the number of such solutions that display appropriate behavior in terms of the discriminant. These estimates sharpen recent results of the author for the general case of arbitrary degree.

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