有限域上三次型零点个数的p-adic估计

p-adic estimate of number of zeros of cubic forms in finite fields

研究有限域上三次型零点个数的p-adic估计问题.改进了经典的Chevalley-Warning定理和Ax-Katz定理关于这类超曲面有理点的估计.

The paper mainly makes a study of the problem of p-adic estimate of the number of zeros of cubic forms in finite field Fq,and improves the classical Chevalley-Warning theorem and Ax-Katz theorem for such hypersurfaces.