On some arithmetic properties of Siegel functions (II)
-
Ho Yun Jung
,
Ja Kyung Koo
Abstract.
Let K be an imaginary quadratic field of discriminant 
.
We deal with problems of constructing normal bases between abelian
extensions of K by making use of singular values of Siegel
functions. First, we find normal bases of ring class fields of
orders of bounded conductors depending on dK over K by using a
criterion deduced from the Frobenius determinant relation. Next,
denoting by 
the ray class field modulo N of K for an
integer 
we consider the field extension
for a prime 
and a positive integer
m relatively prime to p and then find normal bases of all
intermediate fields over 
by utilizing Kawamoto's
arguments. We further investigate certain
Galois module structure of the field extension
with 
, which would be an
extension of Komatsu's work.
© 2014 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Pseudovarieties generated by Brauer type monoids
- On some arithmetic properties of Siegel functions (II)
- Perfect vector alignment of the vorticity and the vortex stretching is one forever
- Frobenius groups of automorphisms and their fixed points
- Schubert calculus and the Hopf algebra structures of exceptional Lie groups
- The sovability of norm, bilinear and quadratic equations over finite fields via spectra of graphs
- Periodicity in the stable representation theory of crystallographic groups
- Sums of Fourier coefficients of a Maass form for SL3(ℤ) twisted by exponential functions
- The rational classification of links of codimension > 2
- On the classifying space for proper actions of groups with cyclic torsion
- Turán determinants of Bessel functions
