An estimate for character sums
An estimate for character sums
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DOI：
10.1090/s0894-0347-1989-0965007-8
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发表时间：
1989-05
影响因子：
3.9
通讯作者：
N. M. Katz
中科院分区：
文献类型：
--
作者：
N. M. Katz
事实证明，考虑以下更一般的情况是有限的领域，n〜1是一个整数，b是f（i，e。 f的扩展，存在k-Algebras b®fk：。= k x k x···· b的detf（t x i b）在b的常规表示中本身具有n个独特的特征值（就上述同构而言，b®f k:。:: = k x k x ... x k，x k，x k，x k，仅当x®1：。:: =（xi' ，x n）具有所有不同组件x j•或均等的x是规则的，并且仅当b等于x生成的f-subalgebra f [x]。元素x是常规的，并且仅当f（x）= E时才是常规的。
It turns out to be easier to consider the following more general situation. F is a finite field, n ~ 1 is an integer, and B is a finite etale F -algebra of dimension n over F (i,e., over a finite extension K of F, there exists an isomorphism of K-algebras B ®F K:.::= K x K x··· x K). We assume given an element x in B that is regular in the sense that its characteristic polynomial detF(T x I B) in the regular representation of B on itself has n distinct eigenvalues. (In terms of the above isomorphism B ® F K :.::= K x K x ... x K, x is regular if and only if x ® 1 :.::= (XI' , •.• x n ) with all distinct components x j • Or equivalently, x is regular if and only if B is equal to the F-subalgebra F[x] generated by x. In the special case when B is a field F , the element x is regular if and only if F(x) = E.)