Kloosterman sums and low complexity sequences

Kloosterman sums much like the Möbius function exhibit plenty of randomness. We formulate the analogues of the Chowla and Sarnak conjectures for the Kloosterman sums and prove them in some cases. For example, we show that Kloosterman sums do not correlate with periodic functions in both vertical and horizontal directions. This is joint work with El H. El Abdalaoui and I. Shparlinski.