Vishnyakova, A.M.Ostrovskii, I.V.Ulanovskii, A.M.2013-05-212013-05-211991Leningrad Math. J., Vol. 2, No. 4https://ekhnuir.karazin.ua/handle/123456789/8527A survey is given of work concerning Linnik's 1960 conjecture on the growth of entire characteristic functions (Fourier transforms) of probability measures. A proof of this conjecture is presented that is substantially shorter and more elementary than the known proofs. With the help of the same idea, new facts are established about the growth of entire characteristic functions with restrictions on the arguments of the zeros.enMathematical analysisArticle