Richard S. Varga, Semi-infinite and infinite strips free of zeros, Rend. Sem. Mat. Univ. e. Politec. Torino 11 (1952), 289-296. MR 14, p. 546. Zbl. 47, p. 315.
For a class of entire functions, which includes ez, we shall show the existence of a semi-infinite strip of non-zero width, symmetric about the non-negative real axis, such that for each entire function in this class, the function and all its partial sums have no zeros in this strip. We shall then show the existence of an infinite strip about the imaginary axis for a class of entire functions, which includes sin z and cos z, for which the same results are true. It will then be shown that the width of the strips obtained is the best possible result.