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On Extremal Polynomials

Published online by Cambridge University Press:  20 November 2018

Kenneth S. Williams
Kenneth S. Williams*
Affiliation:
Carleton University, Ottawa
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Let p denote a prime number and let κp denote the finite field of p elements. Let f(x) ∊ κp[x] be of fixed degree d ≥ 2. We suppose that p is also fixed, large compared with d, say, p ≥ p0(d). By V(f) we denote the number of distinct values of f(x), x ∊ κp. We call f maximal if V(f) = p and quasi-maximal if V(f) = p + O(1). Clearly a maximal polynomial is quasi-maximal but it is not known under what conditions the converse holds.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 4 , October 1967 , pp. 585 - 594
Copyright
Copyright © Canadian Mathematical Society 1967

References

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