Abstract
Let Fq be the finite field,q=pk,with p being a prime and k being a positive integer.Let F*q be the multiplicative group of Fq,that is F*q=Fq\{0}.In this paper,by using the Jacobi sums and an analog of Hasse-Davenport theorem,an explicit formula for the number of solutions of cubic diagonal equation x31+x32+…+x3n=c over Fq is given,where c ∈ F*q and p ≡1(mod 3).This extends earlier results.
基金项目
河南省自然科学基金(232300420123)
国家自然科学基金(12026224)
Research Center of Mathematics and Applied Mathematics,Nanyang Institute of Technology()
NETL
NSTL
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