Article ID Journal Published Year Pages File Type
4583340 Finite Fields and Their Applications 2008 8 Pages PDF
Abstract

Let MnMn be the set of all n×nn×n matrices with entries in the finite field FqFq. Let X(A)X(A) be the degree of the splitting field of the characteristic polynomial of A  , and let μnμn be the average degree:μn=1|Mn|∑A∈MnX(A). A theorem of Reiner is used to prove that, as n→∞n→∞,μn=eBn/logn(1+o(1)), where B is an explicit constant.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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