Displaying similar documents to “Kaplansky's ternary quadratic form.”

Ternary quadratic forms ax² + by² + cz² representing all positive integers 8k + 4

Kenneth S. Williams (2014)

Acta Arithmetica

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Under the assumption that the ternary form x² + 2y² + 5z² + xz represents all odd positive integers, we prove that a ternary quadratic form ax² + by² + cz² (a,b,c ∈ ℕ) represents all positive integers n ≡ 4(mod 8) if and only if it represents the eight integers 4,12,20,28,52,60,140 and 308.

The connection between quadratic forms and the extended modular group

Ahmet Tekcan, Osman Bizim (2003)

Mathematica Bohemica

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In this paper some properties of quadratic forms whose base points lie in the point set F Π ¯ , the fundamental domain of the modular group, and transforming these forms into the reduced forms with the same discriminant Δ < 0 are given.