SMALL ZEROS OF QUADRATIC FORMS MOD P2

Let Q(x) be a quadratic form over ℤ in n variables, p be an odd prime and ∥x∥ = max i |x i |. A solution of the congruence Q(x) ≡ 0 (mod p 2 ) is said to be nontrivial if p ∤ x i for some i. We prove that if this congruence has a nontrivial solution, then it has a nontrivial solution with ∥x∥ ≤ p. W...

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Veröffentlicht in:	Proceedings of the American Mathematical Society 2012-12, Vol.140 (12), p.4041-4052
Hauptverfasser:	COCHRANE, TODD, HAKAMI, ALI H.
Format:	Artikel
Sprache:	eng
Schlagworte:	Abstracting Applied mathematics Hyperplanes Integers Mathematical congruence Mathematical constants Mathematical theorems Nontrivial solutions Number theory Zero
Online-Zugang:	Volltext
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