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. 51–69DOI 10.4171/JEMS/498