Fekete-like polynomials

In 2001, Borwein, Choi, and Yazdani looked at an extremal property of a class of polynomial with ±1 coefficients. Their key result was: Theorem(See Borwein, Choi, Yazdani, 2001.) Let f(z)=±z±z2±⋯±zN−1, and ζ a primitive Nth root of unity. If N is an odd positive integer thenmaxi|f(ζi)|⩾N with equality if and only if N is an odd prime.