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

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DOI

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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     title = {On a {Congruence} {Related} to {Character} {Sums}},
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     year = {1985},
     volume = {28},
     number = {4},
     doi = {10.4153/CMB-1985-052-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1985-052-x/}
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