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Systems of quadratic diophantine inequalities

Wolfgang Müller — 2005

Journal de Théorie des Nombres de Bordeaux

Let Q 1 , , Q r be quadratic forms with real coefficients. We prove that for any ϵ > 0 the system of inequalities | Q 1 ( x ) | < ϵ , , | Q r ( x ) | < ϵ has a nonzero integer solution, provided that the system Q 1 ( x ) = 0 , , Q r ( x ) = 0 has a nonsingular real solution and all forms in the real pencil generated by Q 1 , , Q r are irrational and have rank > 8 r .

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