Ratios of regulators in extensions of number fields
Ratios of regulators in extensions of number fields
复制标题
数域扩展中调节器的比率
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
E. Friedman
中科院分区：
文献类型：
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作者：
A. Costa;E. Friedman
设L/K是数域的扩张。则REG(L)/REG(K)>；C[L Q](LOG IDLI)m，其中REG表示调节子，DL是L的绝对判别式，C[L Q]>；0仅取决于L的次数。如果Lik不属于某些精确定义的扩张无限族，则非负整数m=m(L/K)是正的，类似于CM域，其中REG(L)/REG(K)是常数。这推广了Remak和Silverman的一些不等式，他们假设K是有理域Q，并修改了Berge-Martinet的不等式，他们处理了一般的Lik扩张，但在我们使用绝对扩张的地方使用了它的相对判别式。
Let L/K be an extension of number fields. Then Reg(L)/ Reg(K) > C[L Q](log IDLI)m, where Reg denotes the regulator, DL is the absolute discriminant of L, and C[L Q] > 0 depends only on the degree of L. The nonnegative integer m = m(L/K) is positive if LIK does not belong to certain precisely defined infinite families of extensions, analogous to CM fields, along which Reg(L)/ Reg(K) is constant. This generalizes some inequalities due to Remak and Silverman, who assumed that K is the rational field Q, and modifies those of Berge-Martinet, who dealt with a general extension LIK but used its relative discriminant where we use the absolute one.