Littlewood polynomials with high order zeros
Daniel Berend, Shahar Golan · Mathematics of Computation · 2006
Let N ∗ ( m ) N^{*}(m) be the minimal length of a polynomial with ± 1 \pm 1 coefficients divisible by ( x − 1 ) m (x-1)^m . Byrnes noted that N ∗ ( m ) ≤ 2 m N^{*}(m)\leq 2^m for each m m , and asked whether in fact N ∗ ( m ) = 2 m N^{*}(m)=2^m . Boyd showed that N ∗ ( m ) = 2 m N^{*}(m) = 2^{m} for all m ≤ 5 m \le 5 , but N ∗ ( 6 ) = 48 N^{*}(6) = 48 . He further showed that