Volume 24, Issue 4, September 2017, Pages 545 - 555
The peculiar (monic) polynomials, the zeros of which equal their coefficients
Authors
F. Calogero
Dipartimento di Fisica, Università di Roma “La Sapienza” and Istituto di Fisica Nucleare, Sezione di Roma, Rome, Italy.francesco.calogero@roma1.infn.it,francesco.calogero@uniroma1.it
F. Leyvraz*
Instituto de Física, Universidad Nacional Autónoma de México, Cuernavaca, Morelos 62210, México.f_leyvraz2001@hotmail.com
*
Also at: Centro Internacional de Ciencias, Cuernavaca, Morelos 62210, México
Received 21 May 2017, Accepted 12 June 2017, Available Online 6 January 2021.
- DOI
- 10.1080/14029251.2017.1375690How to use a DOI?
- Keywords
- zeros of polynomials; Ulam polynomials
- Abstract
We evaluate the number of complex monic polynomials, of arbitrary degree N, the zeros of which are equal to their coefficients. In the following, we call polynomials with this property 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.
- Copyright
- © 2017 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC license.
Cite this article
TY - JOUR AU - F. Calogero AU - F. Leyvraz PY - 2021 DA - 2021/01/06 TI - The peculiar (monic) polynomials, the zeros of which equal their coefficients JO - Journal of Nonlinear Mathematical Physics SP - 545 EP - 555 VL - 24 IS - 4 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2017.1375690 DO - 10.1080/14029251.2017.1375690 ID - Calogero2021 ER -