Kloosterman sums in residue classes

Valentin Blomer, Djordje Milićević

Published 2014-10-16Version 1

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.