Subsets of $Z/pZ$ with small Wiener norm and arithmetic progressions

It is proved that any subset of $Z/pZ$, p is a prime number, having small Wiener norm ($l_1$-norm of its Fourier transform) contains a subset which is close to be an arithmetic progression. We apply the obtained results to get some progress in so-called Littlewood conjecture in $Z/pZ$ as well as in a quantitative version of Beurling-Helson theorem.