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.