摘要

Let f(1), ... , f(r) be polynomials in n variables, over the field F-q, and suppose that their degrees are d(1), ... , d(r). It was shown by Warning in 1935 that if N is the number of common zeros of the polynomials f(i), then N >= q(n-d). It is the main aim of the present paper to improve on this bound. When the set of common zeros does not form an affine linear subspace in F-q(n), it is shown for example that N >= 2q(n-d) if q >= 4, and that N >= q(n+1-d)/(n + 2 - d) if the f(i) are all homogeneous.
Bibliography: 5 titles.

  • 出版日期2011