p-dimensionale Vektoren modulo p. II.
Periodic harmonic functions on lattices and points count in positive characteristic
This survey deals with pluri-periodic harmonic functions on lattices with values in a field of positive characteristic. We mention, as a motivation, the game “Lights Out” following the work of Sutner [20], Goldwasser- Klostermeyer-Ware [5], Barua-Ramakrishnan-Sarkar [2, 19], Hunzikel-Machiavello-Park [12] e.a.; see also [22, 23] for a more detailed account. Our approach uses harmonic analysis and algebraic geometry over a field of positive characteristic.
Permutation binomials.
Permutation polynomials in several variables over finite fields
Permutation Polynomials of the Form x... f (x...) and Their Group Structure.
Permutations with coefficients in a subfield
Polynômes de ayant un diviseur de degré donné
Polynômes irréductibles primitifs à coefficients dans un corps fini
Polynômes singuliers à plusieurs variables sur un corps fini et congruences modulo p²
Polynomial Automorphisms Over Finite Fields
It is shown that the invertible polynomial maps over a finite field Fq , if looked at as bijections Fn,q −→ Fn,q , give all possible bijections in the case q = 2, or q = p^r where p > 2. In the case q = 2^r where r > 1 it is shown that the tame subgroup of the invertible polynomial maps gives only the even bijections, i.e. only half the bijections. As a consequence it is shown that a set S ⊂ Fn,q can be a zero set of a coordinate if and only if #S = q^(n−1).
Polynomial cycles in finite extension fields
Polynomial modular n-queens solutions
Polynomial quotients: Interpolation, value sets and Waring's problem
For an odd prime p and an integer w ≥ 1, polynomial quotients are defined by with , u ≥ 0, which are generalizations of Fermat quotients . First, we estimate the number of elements for which for a given polynomial f(x) over the finite field . In particular, for the case f(x)=x we get bounds on the number of fixed points of polynomial quotients. Second, before we study the problem of estimating the smallest number (called the Waring number) of summands needed to express each element of...
Polynomials and linear transformations over finite fields.
Polynomials with minimal value set over Galois rings.
Primitive free quartics with specified norm and trace
Primitive quadratics reflected in -sequences.
Primitive roots and powers among values of polynomials over finite fields.