Article ID Journal Published Year Pages File Type
4595236 Journal of Number Theory 2007 4 Pages PDF
Abstract

In a recent paper [G. Yu, An upper bound for B2[g]B2[g] sets, J. Number Theory 122 (1) (2007) 211–220] Gang Yu stated the following conjecture: Let {pi}i=1∞ be an arbitrary sequence of polynomials with increasing degrees and all coefficients in {0,1}{0,1}. If we denote by (#pi)(#pi) the number of non-zero coefficients of pipi, and let M(pi2) be the maximal coefficient of pi2, thenequation(∗)Q:=lim infi→∞deg(pi)M(pi2)(#pi)2⩾1, as long as (#pi)=o(degpi)(#pi)=o(degpi), as i→∞i→∞. We give an explicit example that shows why this last condition is necessary, and we investigate some open questions it suggests.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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