The distribution of the residues of a quartic polynomial
Glasgow mathematical journal, Tome 8 (1967) no. 2, pp. 67-88
Voir la notice de l'article provenant de la source Cambridge University Press
Let f(x) denote a polynomial of degree d defined over a finite field k with q = pnelements. B. J. Birch and H. P. F. Swinnerton-Dyer [1] have estimated the number N(f) of distinct values of y in k for which at least one of the roots ofis in k. They prove, using A. Weil's deep results [12] (that is, results depending on the Riemann hypothesis for algebraic function fields over a finite field) on the number of points on a finite number of curves, thatwhere λ is a certain constant and the constant implied by the O-symbol depends only on d. In fact, if G(f) denotes the Galois group of the equation (1.1) over k(y) and G+(f) its Galois group over k+(y), where k+ is the algebraic closure of k, then it is shown that λ depends only on G(f), G+(f) and d. It is pointed out that “in general”
McCann, K.; Williams, K. S. The distribution of the residues of a quartic polynomial. Glasgow mathematical journal, Tome 8 (1967) no. 2, pp. 67-88. doi: 10.1017/S0017089500000136
@article{10_1017_S0017089500000136,
author = {McCann, K. and Williams, K. S.},
title = {The distribution of the residues of a quartic polynomial},
journal = {Glasgow mathematical journal},
pages = {67--88},
year = {1967},
volume = {8},
number = {2},
doi = {10.1017/S0017089500000136},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000136/}
}
TY - JOUR AU - McCann, K. AU - Williams, K. S. TI - The distribution of the residues of a quartic polynomial JO - Glasgow mathematical journal PY - 1967 SP - 67 EP - 88 VL - 8 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000136/ DO - 10.1017/S0017089500000136 ID - 10_1017_S0017089500000136 ER -
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