Quaestiones Mathematicae

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On certain character sums

Ganglian Ren, Dingding He, Tianping Zhang


Let q ≥ 2 be an integer, X be a non-principal character mod q, A = A(q)  ≤ q, B = B(q) = q, and H = H(q) ≤ q. In this paper, we shall use the estimates for Kloosterman sums and the properties of trigonometric sums to give some sharp estimates for character sums of the form

Tk(x, A, B,H; q) =       ∑           akX (a),


where h(A,B,H) = {a ∈ Z| (a,q) = 1, 1 ≤ a ≤ A ≤ b ≤ B, ab ≡ (mod, q), |a-b| ≤ H}

Keywords: Character sums, Kloosterman sums, trigonometric sums
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