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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


On constructing fields corresponding to the $ \tilde{A}\sb n$'s of Mestre for odd $ n$

Author: John R. Swallow
Journal: Proc. Amer. Math. Soc. 122 (1994), 85-89
MSC: Primary 12F12; Secondary 11E12, 11R32
MathSciNet review: 1204386
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Abstract: An isomorphism is given between the trace bilinear form of Mestre's $ {A_n}$ extensions over $ \mathbb{Q}(t)$ and a certain quadratic form over $ \mathbb{Q}$ with base field lifted to $ \mathbb{Q}(t)$. This reduces the problem of constructing $ {\tilde A_n}$ extensions from Mestre's $ {A_n}$'s to that of diagonalizing certain forms over $ \mathbb{Q}$. The result expands a result of Schneps.

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PII: S 0002-9939(1994)1204386-7
Article copyright: © Copyright 1994 American Mathematical Society

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