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Saturday, June 14, 2025

Entry 166

The case d=8 is special since it is even but has odd class number h(d)=1. Given the Kronecker symbol (dm), we propose a symmetrical closed-form 

K(k8)=2π161U2(U212+U2+12)2(8m=1[Γ(m8)](8m))1/2=2π161U2(U212+U2+12)2(Γ(18)Γ(38)Γ(58)Γ(78))1/2

with fundamental unit U2=1+2 and form reminiscent of the odd d with class number 1.

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