Coefficients of squares of Newman polynomials
| dc.creator | Kolountzakis, Mihail N. | |
| dc.date | 2008-06-11 | |
| dc.date | 2008-12-07 | |
| dc.date.accessioned | 2026-07-07T12:09:34Z | |
| dc.date.available | 2026-07-07T12:09:34Z | |
| dc.description | We show that there are polynomials $p_N$ of arbitrarily large degree $N$, with coefficients equal to 0 or 1 (Newman polynomials), such that $$ \liminf_{N \to \infty} N \Linf{p_N^2} \bigl / p_N^2(1) < 1, $$ where $\Linf{q}$ denotes the maximum coefficient of the polynomial $q$ and which, at the same time, are sparse: $p_N(1)/N \to 0$. This disproves a conjecture of Yu \cite{yu}. We build on some previous results of Berenhaut and Saidak \cite{berenhaut-saidak} and Dubickas \cite{dubickas} whose examples lacked the sparsity. This sparsity we create from these examples by randomization. | |
| dc.description | Correction of small errors; *Acknowledgement of priority* Results stronger than those contained in this paper, with similar methods, have been obtained by Javier Cilleruelo (cited) before my paper was written. My paper will not be published. Please do not cite it | |
| dc.identifier | https://arxiv.org/abs/0806.1809 | |
| dc.identifier | http://arxiv.org/abs/0806.1809 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209671 | |
| dc.subject | Number Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 11B34 | |
| dc.title | Coefficients of squares of Newman polynomials | |
| dc.type | text |