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摘要
Let f be a polynomial in n variables over the finite field F(q) and N(q)(f) denote the number of F(q)-rational points on the affine hypersurface f = 0 in A(n)(F(q)). A phi-reduction of f is defined to be a transformation sigma : F(q)[ x(1), ... , x(n)] -> F(q)[ x(1), ... , x(n)] such that N(q)(f) - N(q)(sigma(f)) and deg f >= deg sigma(f). In this paper, we investigate phi-reduction by using the degree matrix which is formed by the exponents of the variables of f. With phi-reduction, we may improve various estimates on N(q)(f) and utilize the known results for polynomials with low degree. Furthermore, it can be used to find the explicit formula for N(q)(f).
- 出版日期2011-6
- 单位宁波大学
