Displaying similar documents to “The divisor function over arithmetic progressions”

Kloosterman sums in residue classes

Valentin Blomer, Djordje Milićević (2015)

Journal of the European Mathematical Society

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We prove upper bounds for sums of Kloosterman sums against general arithmetic weight functions. In particular, we obtain power cancellation in sums of Kloosterman sums over arithmetic progressions, which is of square-root strength in any fixed primitive congruence class up to bounds towards the Ramanujan conjecture.

On the fourth-order linear recurrence formula related to classical Gauss sums

Chen Zhuoyu, Zhang Wenpeng (2017)

Open Mathematics

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Let p be an odd prime with p ≡ 1 mod 4, k be any positive integer, ψ be any fourth-order character mod p. In this paper, we use the analytic method and the properties of character sums mod p to study the computational problem of G(k, p) = τk(ψ)+τk(ψ), and give an interesting fourth-order linear recurrence formula for it, where τ(ψ) denotes the classical Gauss sums.