  It is proved that any continuous function f on the unit circle such that the
sequence e^{in f}, n=1,2,... has small Wiener norm \| e^{in f} \|_A = o
(\frac{\log^{1/22} |n|}{(\log \log |n|)^{3/11}}), is linear. Moreover, we get
lower bounds for Wiener norm of characteristic functions of subsets from Z_p in
the case of prime p.
