In this paper, we discuss some relations between zeros of Lucas–Lehmer polynomials and the Gray code. We study nested square roots of 2 applying a “binary code” that associates bits 0 and 1 to “plus” and “minus” signs in the nested form. This gives the possibility to obtain an ordering for the zeros of Lucas–Lehmer polynomials, which take the form of nested square roots of 2.

Ordering of nested square roots of 2 according to the Gray code / Vellucci, Pierluigi; Bersani, Alberto Maria. - In: RAMANUJAN JOURNAL. - ISSN 1382-4090. - STAMPA. - 45:1(2018), pp. 197-210. [10.1007/s11139-016-9862-5]

Ordering of nested square roots of 2 according to the Gray code

VELLUCCI, PIERLUIGI
;
BERSANI, Alberto Maria
2018

Abstract

In this paper, we discuss some relations between zeros of Lucas–Lehmer polynomials and the Gray code. We study nested square roots of 2 applying a “binary code” that associates bits 0 and 1 to “plus” and “minus” signs in the nested form. This gives the possibility to obtain an ordering for the zeros of Lucas–Lehmer polynomials, which take the form of nested square roots of 2.
nested radicals; continued radicals; continued roots; Gray code; zeros of Chebyshev polynomials
01 Pubblicazione su rivista::01a Articolo in rivista
Ordering of nested square roots of 2 according to the Gray code / Vellucci, Pierluigi; Bersani, Alberto Maria. - In: RAMANUJAN JOURNAL. - ISSN 1382-4090. - STAMPA. - 45:1(2018), pp. 197-210. [10.1007/s11139-016-9862-5]
File allegati a questo prodotto
File Dimensione Formato  
Vellucci_Ordering_2018.pdf

solo gestori archivio

Tipologia: Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 885.81 kB
Formato Adobe PDF
885.81 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Vellucci_Preprint_Ordering_2018.pdf

accesso aperto

Tipologia: Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 896.87 kB
Formato Adobe PDF
896.87 kB Adobe PDF Visualizza/Apri PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/927816
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 4
social impact