Littlewood polynomials with high order zeros
نویسندگان
چکیده
منابع مشابه
Littlewood polynomials with high order zeros
Let N∗(m) be the minimal length of a polynomial with ±1 coefficients divisible by (x − 1)m. Byrnes noted that N∗(m) ≤ 2m for each m, and asked whether in fact N∗(m) = 2m. Boyd showed that N∗(m) = 2m for all m ≤ 5, but N∗(6) = 48. He further showed that N∗(7) = 96, and that N∗(8) is one of the 5 numbers 96, 144, 160, 176, or 192. Here we prove that N∗(8) = 144. Similarly, let m∗(N) be the maxima...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2006
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-06-01848-5