Applications of the Hasse–Weil bound to permutation polynomials
| Autor: | Xiang-dong Hou |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Polynomial
Algebra and Number Theory Absolutely irreducible Applied Mathematics 010102 general mathematics General Engineering 0102 computer and information sciences Function (mathematics) 01 natural sciences Theoretical Computer Science Combinatorics Permutation Riemann hypothesis symbols.namesake Finite field 010201 computation theory & mathematics symbols Irreducibility 0101 mathematics Mathematics |
| Zdroj: | Finite Fields and Their Applications. 54:113-132 |
| ISSN: | 1071-5797 |
| DOI: | 10.1016/j.ffa.2018.08.005 |
| Popis: | Riemann's hypothesis on function fields over a finite field implies the Hasse–Weil bound for the number of zeros of an absolutely irreducible bi-variate polynomial over a finite field. The Hasse–Weil bound has extensive applications in the arithmetic of finite fields. In this paper, we use the Hasse–Weil bound to prove two results on permutation polynomials over F q where q is sufficiently large. To facilitate these applications, the absolute irreducibility of certain polynomials in F q [ X , Y ] is established. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect