✦ LIBER ✦
Improvements upon the Chevalley–Warning–Ax–Katz-type estimates
✍ Scribed by Wei Cao; Qi Sun
- Book ID
- 104024724
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 118 KB
- Volume
- 122
- Category
- Article
- ISSN
- 0022-314X
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✦ Synopsis
Let f be a polynomial over finite field F q with q elements and let N(f = 0) denote the number of zeros of f in F q . The q-divisibility properties of N(f = 0) have been studied by many authors, such as Chavelley, Warning, Ax, Katz, etc. In this paper, by reducing the degree of a given polynomial meanwhile remaining the number of its zeros unchanged, we present an improvement upon the Chevalley-Warning-Ax-Katz-type estimates in many cases. Furthermore, our result can improve Cao-Sun's reduction recently obtained on counting the number of zeros of general diagonal equations over finite fields.