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| ON IDEAL CLASS GROUPS AND UNITS IN TERMS OF THE QUADRATIC FORM $x^2+32y^2$ |
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Citation： |
Jurgen HURRELBRINK,YUE Qin.ON IDEAL CLASS GROUPS AND UNITS IN TERMS OF THE QUADRATIC FORM $x^2+32y^2$[J].Chinese Annals of Mathematics B,2005,26(2):239~252 |
| Page view： 1446
Net amount： 883 |
Authors： |
Jurgen HURRELBRINK; YUE Qin |
Foundation： |
Project supported by the National Natural Science Foundation of China (No.10371054) and 02KJB11
006. |
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| Abstract： |
For quadratic number fields $F={\mathbb Q}(\sqrt{2p_1\cdots
p_{t-1}}\,)$ with primes $p_j\equiv 1$ mod 8, the authors study
the class number and the norm of the fundamental unit of $F$. The
results generalize nicely what has been familiar for the fields
${\mathbb Q}(\sqrt{2p}\,)$ with a prime $p\equiv 1$ mod 8,
including density statements. And the results are stated in terms
of the quadratic form $x^2+32y^2$ and illustrated in terms of
graphs. |
Keywords： |
Class group, Redei Matrix, Fundamental unit |
Classification： |
11R70, 11R11, 11R27 |
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