4
$\begingroup$

I'd like to know the name of this kind of polynomial

$p(x)=x^n+a_{1}x^{n-1}+\ldots+a_{n-1}x+1$

where the $a_{i}\in\lbrace0,1\rbrace$.

Thanks.

  • 2
    @A.Neves, if that is the case, you may be interested in knowing (or, of course, you may already know!) that cyclotomic polynomials do have coefficients which are not 0 or$1$(or -1). There is a 2 in the 105th cyclotomic polynomial.2010-09-21

1 Answers 1

13

They're known as Newman polynomials. They are often studied in contexts where one is interested in learning what interesting consequences result from placing such restrictions on the coefficients, for example see here. Erdos and Littlewoood posed several questions about the effects this has on the minimum modulus of the polynomial on the unit circle, e.g. see this paper.

  • 2
    Another link [The Beauty of Roots, John Baez](http://math.ucr.edu/home/baez/roots/)2010-09-23