منابع مشابه
Periods of Iterated Rational Functions over a Finite Field
If f is a polynomial of degree d in Fq[x], let ck(f) be the number of cycles of length k in the directed graph on Fq with edges {(v, f(v))}v∈Fq . For random polynomials, the numbers ck, 1 ≤ k ≤ b, have asymptotic behavior resembling that for the cycle lengths of random functions f : [q] → [q]. However random polynomials differ from random functions in important ways. For example, given the set ...
متن کاملConstructive Analysis of Iterated Rational Functions
We develop the elementary theory of iterated rational functions over the Riemann sphere C∞ in a constructive setting. We use Bishop-style constructive proof methods throughout. Starting from the development of constructive complex analysis presented in [Bishop and Bridges 1985], we give constructive proofs of Montel’s Theorem along with necessary generalisations, and use them to prove elementar...
متن کاملRamification in iterated towers for rational functions
Abstract. Let φ(x) be a rational function of degree > 1 defined over a number field K and let Φn(x, t) = φ (x) − t ∈ K(x, t) where φ(x) is the nth iterate of φ(x). We give a formula for the discriminant of the numerator of Φn(x, t) and show that, if φ(x) is postcritically finite, for each specialization t0 of t to K, there exists a finite set St0 of primes of K such that for all n, the primes d...
متن کاملComputing periods of rational integrals
— A period of a rational integral is the result of integrating, with respect to one or several variables, a rational function over a closed path. This work focuses particularly on periods depending on a parameter: in this case the period under consideration satisfies a linear differential equation, the Picard-Fuchs equation. I give a reduction algorithm that extends the Griffiths-Dwork reductio...
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 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: International Journal of Number Theory
سال: 2017
ISSN: 1793-0421,1793-7310
DOI: 10.1142/s1793042117500713