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Friday, June 13, 2025

Entry 161

Entry 160 dealt with discriminants d with class number 1. Going higher, there are only three fundamental d=4p with class number 2, namely p=5,13,17.  Given the Kronecker symbol (dm), we propose

K(k5)=2π220(1+52)3/4(20m=1[Γ(m20)](20m))1/4K(k13)=2π252(3+132)3/4(52m=1[Γ(m52)](52m))1/4K(k37)=2π2148(6+37)3/4(148m=1[Γ(m148)](148m))1/4

Going to class number 4, the red exponent will now be 1/8.

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