Periods of orbits modulo primes
نویسندگان
چکیده
منابع مشابه
Periods of Orbits modulo Primes
Let S be a monoid of endomorphisms of a quasiprojective variety V defined over a global field K. We prove a lower bound for the size of the reduction modulo places of K of the orbit of any point α ∈ V (K) under the action of the endomorphisms from S. We also prove a similar result in the context of Drinfeld modules. Our results may be considered as dynamical variants of Artin’s primitive root c...
متن کاملPeriods of rational maps modulo primes
Let K be a number field, let φ ∈ K (t) be a rational map of degree at least 2, and let α, β ∈ K . We show that if α is not in the forward orbit of β, then there is a positive proportion of primes p of K such that α mod p is not in the forward orbit of β mod p. Moreover, we show that a similar result holds for several maps and several points. We also present heuristic and numerical evidence that...
متن کاملSome Curious Congruences modulo Primes
Let n be a positive odd integer and let p > n + 1 be a prime. We mainly derive the following congruence: ∑ 0<i1<···<in<p ( i1 3 ) (−1)i1 i1 · · · in ≡ 0 (mod p).
متن کاملFibonacci Numbers modulo Cubes of Primes
Let p be an odd prime. It is well known that Fp−( p 5 ) ≡ 0 (mod p), where {Fn}n>0 is the Fibonacci sequence and (−) is the Jacobi symbol. In this paper we show that if p 6= 5 then we may determine Fp−( p 5 ) mod p3 in the following way:
متن کاملIterations of Integer Polynomial Maps Modulo Primes
In this elementary note we discuss some questions related to the behavior of iterations of polynomial maps with integer coefficients modulo primes. In particular, we introduce three examples of such maps that have interesting dynamical properties. Several open questions are stated and discussed.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2009
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2009.03.007