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Galois Module Structure and Elliptic Functions

โœ Scribed by W. Bley

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
669 KB
Volume
52
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

Let (K) be a quadratic imaginary number field and (R_{f}) the ring class field modulo (f) over (K, f \in \mathbb{N}). Let (\theta_{f}) denote the order of conductor (f) in (K) and let (\mathfrak{g}^{}, \mathrm{~g}) be proper O (\gamma)-ideals such that (\mathbf{g}^{ 2} \subseteq \mathbf{g} \subseteq \mathrm{g}^{*}). Let (\tau) denote the Weber function and let I denote an auxiliary (\mathcal{C}{f})-ideal. For certain extensions (R{f}(\tau(1 \mid \lg )) / R_{f}(\tau(1 \mid \lg ))) it is shown that the ring of integers in (R_{f}(\tau(1 \mid \lg ))) is a free rank one module over the associated order of (R_{f}(\tau(1 \mid \lg )) / R_{f}\left(\tau\left(1 \mid \mathfrak{l g}^{}\right)\right)). 1995 Academic Press, Inc.

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