JournalsjemsVol. 17, No. 1pp. 51–69

Kloosterman sums in residue classes

  • Valentin Blomer

    Georg-August-Universität Göttingen, Germany
  • Djordje Milićević

    Bryn Mawr College, USA
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Abstract

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 xed primitive congruence class up to bounds towards the Ramanujan conjecture.

Cite this article

Valentin Blomer, Djordje Milićević, Kloosterman sums in residue classes. J. Eur. Math. Soc. 17 (2015), no. 1, pp. 51–69

DOI 10.4171/JEMS/498