Journal of Nonlinear Mathematical Physics

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
https://doi.org/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.

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
24 - 4
Pages
545 - 555
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2017.1375690How to use a DOI?
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
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  - https://doi.org/10.1080/14029251.2017.1375690
ID  - Calogero2021
ER  -