Maximal coefficients of squares of Newman polynomials
نویسندگان
چکیده
Newman polynomials are those with all coefficients in {0, 1}. We consider here the problem of finding Newman polynomials P such that all the coefficients of P 2 are so small as possible for deg P and P (1) given. A set A ⊂ [1, N ] is called a B2[g] sequence if every integer n has at most g distinct representations as n = a1 + a2 with a1, a2 ∈ A and a1 ≤ a2. Gang Yu [4] introduced a new idea to obtain the upper bound |A| ≤ √3.2 gN(1 + o(1)) for any B2[g] sequence A ⊂ [1, N ] which improved all the previous ones. It has been conjectured by some authors that the constant 3.2 can be substituted by 2. Gang Yu observed that it would follow from conjecture 1 below.
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A note on the maximal coefficients of squares of Newman polynomials
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