Geodesic
On Extremal Polynomials
Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 585-594

Voir la notice de l'article provenant de la source Cambridge University Press

Let p denote a prime number and let κp denote the finite field ofp elements. Let f(x) ∊ κp[x] be of fixed degree d ≥ 2. We supposethat p is also fixed, large compared with d, say, p ≥ p0(d). ByV(f) we denote the number of distinct values of f(x), x ∊ κp. Wecall f maximal if V(f) = p and quasi-maximal if V(f) = p + O(1). Clearly amaximal polynomial is quasi-maximal but it is not known under whatconditions the converse holds. 
Williams, Kenneth S. On Extremal Polynomials. Canadian mathematical bulletin, Tome 10 (1967) no. 4, pp. 585-594. doi: 10.4153/CMB-1967-057-8
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[1] 1. Birch, B. J. and Lewis, D. J., £ - adic forms. Jour. Indian Math. Soc, 23 (1955), 11-32. Google Scholar

[2] 2. Bombieri, E. and Davenport, H., On two problems of Mordell. Amer. J. Math., 88 (1966), 61-70. Google Scholar

[3] 3. Carlitz, L. and Uchiyama, S., Bounds for exponential sums. Duke Math. Jour., 24 (1955), 37-41. Google Scholar

[4] 4. Chalk, J. H.H. and Williams, K. S., The distribution of solutions of congruences. Mathematika, 12 (1966), 176-192. Google Scholar

[5] 5. Davenport, H. and Lewis, D. J., Notes on congruences I. Quart. J. Math. Oxfor. (2), 14 (1966), 51-60. Google Scholar

[6] 6. Dickson, L. E., Linear groups. Dover Publications, Inc., N. Y. (1955), 54-64. Google Scholar

[7] 7. Mordell, L. J., A congruence problem of E. G. Straus. Jour. Lond. Math. Soc, 38 (1966), 108-110. Google Scholar

[8] 8. Mordell, L. J., On the least residue and non - residue of a polynomial. Jour. Lond. Math. Soc, 38 (1966), 451-453. Google Scholar

[9] 9. Williams, K. S., The distribution of the residues of aquartic polynomial. To appear in the Glasgow Math. Jour. Google Scholar

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