Rechnen in endlichen Körpern (Beispiele elementarer Zahlentheorie).
Rédei-Permutationen auf Restklassenringen Z/(m).
Reduction formulas for certain multiple exponential sums
Reguläre Polynome über endlichen Körpern
Remarks on Hua's estimate of complete trigonometrical sums
Répartition modulo 1 dans un corps de séries formelles sur un corps fini [Book]
Répartition modulo 1 dans un corps de séries formelles sur un corps fini
Introduction. Soit q une puissance d’un nombre premier p et soit le corps fini à q éléments. Une certaine analogie entre l’arithmétique de l’anneau ℤ des entiers rationnels et celle de l’anneau a conduit à étendre à de nombreuses questions de l’arithmétique classique. L’équirépartition modulo 1 est une de ces questions. Le corps des nombres réels est alors remplacé par le corps des séries de Laurent formelles, complété du corps des fractions rationnelles pour la valuation à l’infini et...
Resolution of the sign ambiguity in the determination of the cyclotomic numbers of order 4 and the corresponding Jacobsthal sum.
Roth's theorem on systems of linear forms in function fields
Schrödinger Equation and Oscillatory Hilbert Transforms of Second Degree.
Self-reciprocal polynomials over finite fields.
Sequences of reducible -polynomials modulo a prime.
Shtukas and Jacobi sums.
Sidon basis in polynomial rings over finite fields
Let denote the polynomial ring over , the finite field of elements. Suppose the characteristic of is not or . We prove that there exist infinitely many such that the set contains a Sidon set which is an additive basis of order .
Singular moduli and supersingular moduli of Drinfeld modules.
Solving quadratic equations over polynomial rings of characteristic two.
We are concerned with solving polynomial equations over rings. More precisely, given a commutative domain A with 1 and a polynomial equation antn + ...+ a0 = 0 with coefficients ai in A, our problem is to find its roots in A.We show that when A = B[x] is a polynomial ring, our problem can be reduced to solving a finite sequence of polynomial equations over B. As an application of this reduction, we obtain a finite algorithm for solving a polynomial equation over A when A is F[x1, ..., xN] or F(x1,...
Some Algebraic Properties of Polynomial Rings
In this article we extend the algebraic theory of polynomial rings, formalized in Mizar [1], based on [2], [3]. After introducing constant and monic polynomials we present the canonical embedding of R into R[X] and deal with both unit and irreducible elements. We also define polynomial GCDs and show that for fields F and irreducible polynomials p the field F[X]/ is isomorphic to the field of polynomials with degree smaller than the one of p.
Some congruences for binomial coefficients
Some doubly exponential sums over ℤₘ
Some generalisations of Chebyshev polynomials and their induced group structure over a finite field