Further improvements to the Chevalley-Warning theorems
نویسندگان
چکیده
We study lower bound estimates for the number of solutions systems equations over finite fields. Heath-Brown improved bounds given by classical Chevalley-Warning Theorems excluding whose form an affine space. improve each Heath-Brown's results and demonstrate sharpness in several cases.
منابع مشابه
A Note on the Chevalley–Warning Theorems
The most widely known result of Chevalley–Warning type states that if one has a polynomial over a finite field of characteristic p, and the number of variables exceeds the degree, then the number of zeros is a multiple of p. In particular, if the polynomial is homogeneous, there is at least one non-trivial zero. There are a number of related results in the literature. Generally, let Fq be a fin...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2023
ISSN: ['1090-2465', '1071-5797']
DOI: https://doi.org/10.1016/j.ffa.2023.102194