A property of entire functions with real taylor coefficients

Suppose thatf(z) is an entire transcendental function with real Taylor coefficients, M(r)= max¦f(z)¦on¦z¦=r, and {_n} is the sequence of sign changes of the coefficients. We will show that if (1/_n)<, then.Translated from Matematicheskie Zametki, Vol. 18, No. 3, pp. 395–402, September, 1975.The author thanks A. A. Gol'dberg for his useful comments.