Number of Solutions for a Class of Diagonal Cubic Equations over Finite Fields
In this paper,by using the properties of Gauss sum and Jacobi sum,we give the so-lution B(n,m)of a class of diagonal cubic equation x31+x32+…+x3n+z(y31+y32+…+y3m)=0 over finite field Fq with variable xi,yj ∈ Fq(i=1,2,…,n;j=1,2,…,m),and obtain the explicit expression of generating function∞∑m-1∞∑n-1B(n,m)xnym,where q=pk,p is a prime number,k is a positive integer.
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