An estimate of the Hecke L-functions on the critical line

One obtains, under certain restrictions, an estimate for the Hecke L -functions on the critical line, similar to the estimate for the Riemann zeta-function.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 91, pp. 40–51, 1979.In conclusion, I would like to express my gratitude to A. I. Vinogradov for his constant interest and help in the writing of this paper.