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Proceedings of ASARC Workshop Daecheon & Muju 2009
(2009 / vol.11 / no.2)
Normal bases of ray class fields over imaginary quadratic fields
Ho Yun Jung, Ja Kyung Koo, Dong Hwa Shin
Pages. 95-108   



We first develop a criterion to determine normal bases (Theorem

ef{criterion}), and by making use of necessary lemmas which were
refined from cite{J-K-S} we further prove that singular values of
certain Siegel functions form normal bases of ray class fields over
all imaginary quadratic fields other than $mathbb{Q}(sqrt{-1})$
and $mathbb{Q}(sqrt{-3})$ (Theorem
ef{main} and Remark

ef{remaining}). This result would be an answer for the
Lang-Schertz conjecture (cite{Lang} p. 292 or cite{Schertz} p.
386) on a ray class field with any modulus generated by an integer
$geq2$ (Remark
ef{S-Rinvariant}).



1. Introduction
2. A criterion to determine normal bases
3. Action of Galois groups
4. Normal bases of $K_{(N)}$ over $K$



class fields, modular forms and functions, normal bases



11F11, 11F20, 11R37, 11Y40