LOCAL CORRECTIONS OF DISCRIMINANT BOUNDS AND SMALL DEGREE EXTENSIONS OF QUADRATIC BASE FIELDS
LOCAL CORRECTIONS OF DISCRIMINANT BOUNDS AND SMALL DEGREE EXTENSIONS OF QUADRATIC BASE FIELDS
复制标题
二次基场判别界的局部修正和小度扩张
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
D. Doud
中科院分区：
文献类型：
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作者：
S. Brueggeman;D. Doud
利用Odlyzko和Poitou的分析技巧，我们建立了数域的判别式的下界表，包括对已知范数的理想的局部修正。将这些表中得到的下界与从涉及不同的计算中得到的数域的判别式的上界进行比较，我们证明了具有有限分支的二次域的一些小度扩张是不存在的。我们注意到，我们的几个结果需要局部校正的界限。
Using analytic techniques of Odlyzko and Poitou, we create tables of lower bounds for discriminants of number fields, including local corrections for ideals of known norm. Comparing the lower bounds found in these tables with upper bounds on discriminants of number fields obtained from calculations involving differents, we prove the nonexistence of a number of small degree extensions of quadratic fields having limited ramification. We note that several of our results require the locally corrected bounds.