Hostname: page-component-686fd747b7-4b24c Total loading time: 0 Render date: 2025-02-13T13:26:27.449Z Has data issue: false hasContentIssue false
  • English
  • Français

Note on Factorable Polynomials

Published online by Cambridge University Press:  20 November 2018

Kenneth S. Williams
Kenneth S. Williams*
Affiliation:
Summer Research Institute Queen's University, Kingston
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X1, X2,…, Xk, denote k ≥ 2 indeterminates and let f(X1,…, Xk) be a homogeneous polynomial, in GF(pn) [X1,…, Xk], which is irreducible but not absolutely irreducible over GF(pn). Thus f is irreducible in GF(pn)[X1,…, Xk] but reducible in some GF(pnm) [X1,…, Xk], m > 1. For any polynomial h(X1,…, Xk) in GF(pnℓ)[X1,…, Xk, ℓ ≥ 1, let Npn(h) denote the number of (x1,…, xk) ∈ GF(pn)×…× GF(pn) such that (hx1…, xk) = 0.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 12 , Issue 5 , October 1969 , pp. 589 - 595
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Birch, B.J. and Lewis, D. J., p-adic forms. J. Indian Math. Soc. 23 (1959) 11–32.Google Scholar
2. Carlitz, L., On factorable polynomials in several indeterminates. Duke Math. J. 2 (1936) 660–670.Google Scholar
3. Carlitz, L., The number of solutions of some special equations in a finite field. Pacific J. Math. 4 (1954) 207–217.Google Scholar