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. In particular, 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.