Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4582696 | Finite Fields and Their Applications | 2016 | 5 Pages |
Abstract
Let v be the number of distinct values of the polynomial f(x)=x4+ax2+bxf(x)=x4+ax2+bx, where a and b are elements of the finite field of size q, where q is odd. When b is 0, an exact formula for v can be given. When b is not 0, v=(5/8)q+O(q), where the error term comes from the Riemann hypothesis. In this note we establish for the case that b is not 0, the inequality v≥(q+1)/2v≥(q+1)/2, without relying on the Riemann hypothesis.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Robert C. Valentini,