About the life and activities of academician Zarullo Husenovich Rakhmonov

The article is devoted to the doctor of physico-mathematical Sciences, academician of the Academy of Sciences of the Republic of Tajikistan, one of the foremost experts in the field of number theory, Zarullo Husenovich Rakhmonov in connection with his 60–year anniversary. Provides a brief biography, the main stages of development of his scientific career. We give the review of results of Z. H. Rakhmonov on following problems: on the distribution of the Goldbach's and Hardy–Littlewood's numbers in short arithmetical progressions, on the problem of mean values of the Chebyshev's function and the problem of the Riemann zeta-function zeros belonging to short rectangular in the critical strip, to estimations short trigonometric sums over primes and on the Goldbach's problem with almost equals summands, on the Selberg's problem concerning to the Riemann's zeta-function zeros lying on short intevals of the critical line. In conclusion, the author presents a list of main scientific publications Z. H. Rakhmonov.