Geodesic
On a Congruence Related to Character Sums
Canadian mathematical bulletin, Tome 28 (1985) no. 4, pp. 431-439

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

If χ is a Dirichlet character to a prime-power modulus p α, then the problem of estimating an incomplete character sum of the form ∑1≤x≤h χ (x) by the method of D. A. Burgess leads to a consideration of congruences of the type f(x)g'(x) - f'(x)g(x) ≡ 0(pα),where fg(x) ≢ 0(p) and f, g are monic polynomials of equal degree with coefficients in Ζ. Here, a characterization of the solution-set for cubics is given in terms of explicit arithmetic progressions.
DOI : 10.4153/CMB-1985-052-x
Mots-clés : 10A10, 10G05 
Chalk, J. H. H. On a Congruence Related to Character Sums. Canadian mathematical bulletin, Tome 28 (1985) no. 4, pp. 431-439. doi: 10.4153/CMB-1985-052-x
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[1] 1. Burgess, D.A., On Character Sums and L-series, Proc. London Math. Soc, (3), 12 (1962), pp. 193–196. Google Scholar

[2] 2. Chalk, J.H.H., A New Proof of Burgess’ Theorem on Character Sums, C-R Math, Rep. Acad. Sci. Canada, No. 4 V (1983), pp. 163–168, (see Math. Reviews for a revised statement of the result). Google Scholar

[3] 3. Chalk, J.H.H. and Smith, R.A., Sándor's Theorem on Polynomial Congruences and Hensel's Lemma, C-R Math. Rep. Acad. Sci. Canada, No. 1, II (1982), pp. 49–54. Google Scholar

[4] 4. Davenport, H. and P. Erdös, The Distribution of Quadratic and Higher Residues, Publications Math ematicae, T-2, fasc, 3-4 (1952), pp. 252–265. Google Scholar

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