Kloosterman sums in residue classes
  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. 
Valentin Blomer and Djordje Mili\'cevi\'c
math.NT