Dohmae, Kazuhiro A note on Sinnott’s index formula. (English) Zbl 0887.11046 Acta Arith. 82, No. 1, 57-67 (1997). Let \(K\) be an imaginary, abelian number field with conductor \(m= p_1^{e_1} p_2^{e_2}\). Supposing that the maximal subfields of \(K\) with conductor a prime power are also imaginary, K. Dohmae [J. Number Theory 61, 343-364 (1996; Zbl 0869.11082)] found a basis for the group of circular units of \(K\) and a simple, direct proof for Sinnott’s class number formula. Dropping the above supposition, the present paper yields analogous results. In particular, one obtains \(g'=\delta_p + \delta_q\), which makes these 3 parameters disappear in Sinnott’s index formula (compare Theorems 4.1 and 5.1 in [W. Sinnott, Invent. Math. 62, 181-234 (1980; Zbl 0465.12001)]). Reviewer: G.Lettl (Graz) Cited in 3 Documents MSC: 11R27 Units and factorization 11R29 Class numbers, class groups, discriminants 11R20 Other abelian and metabelian extensions Keywords:circular units; class number; imaginary abelian number field; Sinnott’s index formula Citations:Zbl 0465.12001; Zbl 0869.11082 × Cite Format Result Cite Review PDF Full Text: DOI EuDML