ROOTS OF POLYNOMIALS OF BOUNDED HEIGHT

Let V be the set of roots of {-1, 0, 1} polynomials. Each a E V must be a unit which lies with its conjugates in the annulus 1/2 < vertical bar z vertical bar < 2. We begin with an explicit example showing that this condition is not sufficient. Furthermore, for each (sic) is an element of (1, 2], we show that the set of units that lie with their conjugates in 1/(sic) < vertical bar z vertical bar < (sic) but do not belong to V is everywhere dense in the annulus 1/(sic) <= vertical bar z vertical bar <= (sic). This is derived from our main result claiming that the number alpha e(2 pi il/p) is not a root of a nonzero integer polynomial of height <= H if p is a sufficiently large prime number, l < p is a positive integer, and alpha not equal 0 is an algebraic number having at least one conjugate of modulus not equal 1.