Cycles of polynomial mappings in several variables.
Cycles of polynomial mappings in two variables over rings of integers in quadratic fields
We find all possible cycle-lengths for polynomial mappings in two variables over rings of integers in quadratic extensions of rationals.
Polynomial cycles in certain local domains
1. Let R be a domain and f ∈ R[X] a polynomial. A k-tuple of distinct elements of R is called a cycle of f if for i=0,1,...,k-2 and . The number k is called the length of the cycle. A tuple is a cycle in R if it is a cycle for some f ∈ R[X]. It has been shown in [1] that if R is the ring of all algebraic integers in a finite extension K of the rationals, then the possible lengths of cycles of R-polynomials are bounded by the number , depending only on the degree N of K. In this note we consider...
Cycles of polynomials in algebraically closed fields of positive characteristic
Cycles of polynomials in algebraically closed fields of positive characteristic (II)
Cycles of polynomial mappings in several variables over rings of integers in finite extensions of the rationals
Finite Polynomial Orbits in Finitely Generated Domains.
On prime values of reducible quadratic polynomials
It is shown that Dickson’s Conjecture about primes in linear polynomials implies that if f is a reducible quadratic polynomial with integral coefficients and non-zero discriminant then for every r there exists an integer such that the polynomial represents at least r distinct primes.
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