Zur Verteilung der Quadrate ganzer Zahlen in rationalen Quaternionenalgebren

For γ ∈ ?letQ 〈γ〉 = ?i]+?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 t0.315, C_γ, D_γ > 0 are numerical constants, and c, d are given by c := π(1 + log 2 - 2η) and d := π2(1 + 4 log 4 - 4π)/8, where π = 0.577 … is Euler’s constant.