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Let be a finite abelian extension of an imaginary quadratic number field . Let denote a prime ideal of lying over the rational prime . We assume that splits completely in and that does not divide the class number of . If is split in the first named author has adapted a construction of Solomon to obtain elliptic -units in . In this paper we generalize this construction to the non-split case and obtain in this way a pair of elliptic -units depending on a choice of generators of a certain Iwasawa algebra (which here is of rank 2). In our main result we express the -adic valuations of these -units in terms of the -adic logarithm of an explicit elliptic unit. The crucial input for the proof of our main result is the computation of the constant term of a suitable Coleman power series, where we rely on recent work of T. Seiriki.
Information
Published: 1 January 2020
First available in Project Euclid: 12 January 2021
Digital Object Identifier: 10.2969/aspm/08610079
Subjects:
Primary:
11G15
,
11G16
,
11R27
Keywords:
Coleman power series
,
Elliptic units
,
Iwasawa theory