Normal bases of ray class fields over imaginary quadratic fields

Details Normal bases of ray class fields over imaginary quadratic fields Normal bases of ray class fields over imaginary quadratic fields

2010-07-14

arxiv.org/abs/1007.2312v2

Mathematics

Number Theory

Scientific paper

We develop a criterion for a normal basis, and prove that the singular values
of certain Siegel functions form normal bases of ray class fields over
imaginary quadratic fields other than $\mathbb{Q}(\sqrt{-1})$ and
$\mathbb{Q}(\sqrt{-3})$. This result would be an answer for the Lang-Schertz
conjecture on a ray class field with modulus generated by an integer ($\geq2$).

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