Polynomials with coefficients from a finite set

This paper focuses on the problem concerning the location and the number of zeros of those polynomials when their coefficients are restricted with special conditions. The problem of the number of the zeros of reciprocal Littlewood polynomials on the unit circle is discussed, the interest on bounds for the number of the zeros of reciprocal polynomials on the unit circle arose after 1950 when Erdos began introducing problems on zeros of various types of polynomials. Our main result is the problem of finding the number of zeros of complex polynomials in an open disk.