Density of periodic points for Lattès maps over finite field

Autor:	Karina Cho, Trevor Hyde, Bianca Thompson, Chieh-Mi Lu, Zoë Bell, Eric Zhu, Jasmine Camero
Rok vydání:	2022
Předmět:	Elliptic curve Pure mathematics Algebra and Number Theory Finite field Endomorphism Simple (abstract algebra) Periodic point Supersingular elliptic curve Prime (order theory) Mathematics
Zdroj:	Journal of Number Theory. 238:951-966
ISSN:	0022-314X
DOI:	10.1016/j.jnt.2021.10.009
Popis:	Let L d be the Lattes map associated to the multiplication-by-d endomorphism of an elliptic curve E defined over a finite field F q . We determine the density δ ( L d , q ) of periodic points for L d in P 1 ( F q ) . We show that the periodic point densities δ ( L d , q n ) converge as n → ∞ along certain arithmetic progressions, and compute simple explicit formulas for δ ( L l , q ) when l is a prime and E belongs to a special family of supersingular elliptic curves.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::c277aa730c5fdddd1f6876270849a5f7 https://doi.org/10.1016/j.jnt.2021.10.009 Zobrazit plný text záznamu Full Text from ScienceDirect