Abstract

For γ ∈ ℤletQ 〈γ〉 = ℚ[i]+ℚ[i]j. where j. is a hypercomplex number withj2 = γ, and define addition and multiplication formally with respect to\(zj = j\overline z \)for all z ∈ ™[i], so thatQ〈γ〉 becomes a quaternion algebra over the rationals. Further fix γ s.t.Q 〈γ 〉 is a division algebra and define for real X ≥ 1 Open image in new window where Open image in new window |Re(α)|, |Im(α)|, |Re(β)|, |Im(o)|≤ X and Open image in new window

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