A minimax problem about unit vectors in the plane

초록

For n greater than or equal to 2, we obtain the extremal values of the minimax problem for exponential sums mu(n) := min max(\x\=1){\Sigma(k=0)(n-1)x(k)\, \Sigma(k=0)(n-1)x(kn)\}. Moreover, we show that the polynomial with coefficients 0 and 1 derived from mu(n) does not have zeros on the unit circle.