The Mahler Problem with Nonmonotone Right-Hand Side in the Field of Complex Numbers

In the last twenty years, the exact order of approximation by zeros of the moduli of the values of the integer polynomials in a real and a complex variable was established. However, in the case of convergence of the series consisting of the right-hand sides of inequalities, the monotonicity condition for the right-hand sides in the classical Khintchine theorem can be dropped. It is shown in the present paper that, in the complex case, the monotonicity condition is also insignificant for polynomials of arbitrary degree.