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Lower powers of elliptic units. (English) Zbl 1003.11026
The authors construct products of singular values of the Klein form and prove that these values are contained in ray class fields over imaginary quadratic fields. From the calculated examples one sees that in these cases the singular values generate the corresponding ray class field. The authors conjecture that this is always the case.

MSC:
11G16 Elliptic and modular units
11R27 Units and factorization
11Y40 Algebraic number theory computations
11R37 Class field theory
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References:
[1] Deuring, M., Die Klassenkörper der komplexen Multiplikation. Enzykl. d. math. Wiss.1/2, 2. Aufl., Heft 10, Stuttgart, 1958. · Zbl 0123.04001
[2] Lang, S., Elliptic functions. Addison Wesley, 1973. · Zbl 0316.14001
[3] Meyer, C., Über einige Anwendungen Dedekindscher Summen. Journal Reine Angew. Math.198 (1957), 143-203. · Zbl 0079.10303
[4] Robert, G., La racine 12-ième canonique de Δ(L)[L:L]/Δ(L)Sém. de th. des nombresParis, 1989-90.
[5] Schertz, R., Niedere Potenzen elliptischer Einheiten. Proc. of the International Conference on Class Numbers and Fundamental Units of Algebraic Number Fields, Katata, Japan (1986), 67-87. · Zbl 0615.12013
[6] Schertz, R., Construction of Ray Class Fields by Elliptic Units. J. Théor. Nombres Bordeaux9 (1997), 383-394. · Zbl 0902.11047
[7] Stark, H., L-functions at s = 1, IV. Adv. Math.35 (1980), 197-235. · Zbl 0475.12018
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