No CrossRef data available.
Article contents
Distinct Values of a Polynomial in Subsets of a Finite Field
Published online by Cambridge University Press: 20 November 2018
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.
If A is a set with only a finite number of elements, we write |A| for the number of elements in A. Let p be a large prime and let m be a positive integer fixed independently of p. We write [pm] for the finite field with pm elements and [pm]′ for [pm] – {0}. We consider in this paper only subsets H of [pm] for which |H| = h satisfies
1.1
If f(x) ∈ [pm, x] we let N(f; H) denote the number of distinct values of y in H for which at least one of the roots of f(x) = y is in [pm]. We write d(d ≥ 1) for the degree of f and suppose throughout that d is fixed and that p ≧ p0(d), for some prime p0, depending only on d, which is greater than d.
- Type
- Research Article
- Information
- Copyright
- Copyright © Canadian Mathematical Society 1969
References
1.
Carlitz, L. and Uchiyama, S., Bounds for exponential sums, Duke Math. J.
24 (1957), 37–41.Google Scholar
2.
McCann, K. and Williams, K. S., The distribution of the residues of a quartic polynomial, Glasgow Math. J.
8 (1967), 67–88.Google Scholar
2.
Uchiyama, S., Note on the mean value of V(f), Proc. Japan Acad.
81 (1955), 199–201.Google Scholar
You have
Access