Cyclotomic unit index formula
= Cyclotomic unit index formula
{title2=$v_p[\mathcal O_{K_n^+}^{\times}:D_n]=v_p(h_{K_n^+})$}
For a real cyclotomic field of odd prime-power conductor, the index of its cyclotomic-unit group has the same p-part as its ideal class number. The <analytic class number formula> compares the regulator of all units with the explicit cyclotomic-unit regulator. The equality here is stated at the p-part level, so harmless prime-to-p normalization factors do not affect it.