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On a Congruence Related to Character Sums
Published online by Cambridge University Press: 20 November 2018
Abstract
If χ is a Dirichlet character to a prime-power modulus pα, 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.
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- Copyright © Canadian Mathematical Society 1985
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