A note on the maximal coefficients of squares of Newman polynomials

✍ Scribed by K.S. Berenhaut; F. Saidak

• Book ID: 104024805
• Publisher: Elsevier Science
• Year: 2007
• Tongue: English
• Weight: 90 KB
• Volume: 125
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2006.09.015

✦ Synopsis

In a recent paper [G. Yu, An upper bound for B 2 [g] sets, J. Number Theory 122 (1) (2007) 211-220] Gang Yu stated the following conjecture: Let {p i } ∞ i=1 be an arbitrary sequence of polynomials with increasing degrees and all coefficients in {0, 1}. If we denote by (#p i ) the number of non-zero coefficients of p i , and let M(p 2 i ) be the maximal coefficient of p 2 i , then

as long as (#p i ) = o(deg p i ), as i → ∞. We give an explicit example that shows why this last condition is necessary, and we investigate some open questions it suggests.