Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5771623 | Finite Fields and Their Applications | 2017 | 7 Pages |
Abstract
Let v be the number of distinct values of the polynomial f(x)=x4+ax2+bx, where a and b are elements of the finite field k of size q, where q is odd. When b is 0, an exact formula for v can be given. When b is not 0, as a consequence of the Tchebotarev Density Theorem, v=(5/8)q+O(q). When the Galois closure of k(x)/k(f(x)) is a rational function field, v can be determined exactly. In this work we determine those f(x)'s for which this occurs and give the formula for v.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Robert C. Valentini,