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Quadratic Diophantine Inequalities

✍ Scribed by D.Eric Freeman

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
258 KB
Volume
89
Category
Article
ISSN
0022-314X

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✦ Synopsis

We consider systems of quadratic diophantine inequlities. For example, suppose that Q 1 and Q 2 are real diagonal quadratic forms in s variables, where one has s 10. Suppose also that every form :Q 1 +;Q 2 with (:, ;) # R 2 "[0] has at least 5 nonzero coefficients, one irrational coefficient, at least one negative coefficient, and at least one positive coefficient. Then for any =>0, there exists a nonzero integral vector x # Z s such that |Q 1 (x)| <= and |Q 2 (x)| <=. We also prove a result on systems of R quadratic diophantine inequalities under more complicated restrictions.

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