Name
Title | ||
|---|---|---|
Square root Bound on the Least Power Non-residue using a Sylvester-Vandermonde Determinant |
Abstract | ||
|---|---|---|
We give a new elementary proof of the fact that the value of the least $k^{th}$ power non-residue in an arithmetic progression $\{bn+c\}_{n=0,1...}$, over a prime field $\F_p$, is bounded by $7/\sqrt{5} \cdot b \cdot \sqrt{p/k} + 4b + c$. Our proof is inspired by the so called \emph{Stepanov method}, which involves bounding the size of the solution set of a system of equations by constructing a non-zero low degree auxiliary polynomial that vanishes with high multiplicity on the solution set. The proof uses basic algebra and number theory along with a determinant identity that generalizes both the Sylvester and the Vandermonde determinant. |
Year | Venue | Keywords |
|---|---|---|
2011 | Clinical Orthopaedics and Related Research | arithmetic progression,number theory,symbolic computation,vandermonde determinant,system of equations |
Field | DocType | Volume |
Discrete mathematics,Combinatorics,Algebra,Elementary proof,Multiplicity (mathematics),Elementary algebra,Vandermonde matrix,Solution set,Number theory,Mathematics,Arithmetic progression,Bounded function | Journal | abs/1104.4 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Michael Forbes | 1 | 0 | 0.34 |
| Neeraj Kayal | 2 | 263 | 19.39 |
| Rajat Mittal | 3 | 170 | 17.59 |
| Chandan Saha | 4 | 227 | 16.91 |