MULTIPLICATIVE ORDERS IN ORBITS OF POLYNOMIALS OVER FINITE FIELDS
2017 ◽
Vol 60
(2)
◽
pp. 487-493
◽
Keyword(s):
AbstractWe show, under some natural restrictions, that orbits of polynomials cannot contain too many elements of small multiplicative order modulo a large prime p. We also show that for all but finitely many initial points either the multiplicative order of this point or the length of the orbit it generates (both modulo a large prime p) is large. The approach is based on the results of Dvornicich and Zannier (Duke Math. J.139 (2007), 527–554) and Ostafe (2017) on roots of unity in polynomial orbits over the algebraic closure of the field of rational numbers.
1990 ◽
Vol 49
(2)
◽
pp. 309-318
◽
1999 ◽
Vol 42
(1)
◽
pp. 78-86
◽
Keyword(s):
2020 ◽
Vol 102
(3)
◽
pp. 365-373
2001 ◽
Vol 21
(3)
◽
pp. 412-416
◽
2012 ◽
Vol 18
(1)
◽
pp. 108-122
◽
Keyword(s):
1993 ◽
Vol 119
(3)
◽
pp. 711-711
◽
2017 ◽
Vol 24
(1)
◽
pp. 87-95