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arXiv · 1706.03405

The peculiar (monic) polynomials, the zeros of which equal their coefficients

Francesco Calogero·Francois Leyvraz
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Abstract

We evaluate the number of monic polynomials (of arbitrary degree $N$) the zeros of which equal their coefficients when these are allowed to take arbitrary complex values. In the following, we call polynomials with this property {\em peculiar\/} polynomials. We further show that the problem of determining the peculiar polynomials of degree $N$ simplifies when any of the coefficients is either 0 or 1. We proceed to estimate the numbers of peculiar polynomials of degree $N$ having one coefficient zero, or one coefficient equal to one, or neither.

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Francesco Calogero, Francois Leyvraz. 2017-06-11. The peculiar (monic) polynomials, the zeros of which equal their coefficients. https://arxiv.org/abs/1706.03405

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