THE S-MEASURE FOR ALGEBRAIC INTEGERS HAVING ALL THEIR CONJUGATES IN A SECTOR

Let alpha be a nonzero algebraic integer of degree d, all of whose conjugates alpha(1) = alpha, alpha(2), ..., alpha(d) lie in a sector vertical bar arg z vertical bar <= theta, 0 < theta <= 90 degrees. We define the S-measure of alpha by S(alpha) = Sigma(d)(i=1) vertical bar alpha(i)vertical bar and the absolute S-measure of alpha by s(alpha) = S (alpha)/d. We compute the greatest lower bound c(theta) of s(alpha) for alpha belonging to twelve subintervals of (0, theta). Among these subintervals, three are complete. These computations use the principle of explicit auxiliary functions and our recursive algorithm.