Résultants cycliques et polynômes cyclotomiques
Résultats et problèmes en théorie des nombres
Results on disjoint covering systems on the ring of integers
Results on the ratios of the terms of second order linear recurrences
Řetězové zlomky [Book]
Riordan arrays, orthogonal polynomials as moments, and Hankel transforms.
Rogers-Ramanujan-Slater type identities.
Root location for the characteristic polynomial of a Fibonacci type sequence
We analyse the roots of the polynomial for . This is the characteristic polynomial of the recurrence relation for , which includes the relations of several particular sequences recently defined. In the end, a matricial representation for such a recurrence relation is provided.
Roots of increasing sequences.
Rota-Baxter operators and Bernoulli polynomials
We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and Bernoulli polynomials. We show how Rota-Baxter operators equalities rewritten in terms of Bernoulli polynomials generate identities for the latter.
Rotations sur les groupes, nombres algébriques, et substitutions
Running modulus recursions.
Sárközy's theorem for 𝓟-intersective polynomials
Scharfe untere Abschätzung für die Anzahlfunktion der B-Zwillinge
Schinzel's conjecture H and divisibility in abelian linear recurring sequences
Score lists in bipartite multi hypertournaments
Searching for Diophantine quintuples
We consider Diophantine quintuples a, b, c, d, e. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most Diophantine quintuples.
Secant tree calculus
A true Tree Calculus is being developed to make a joint study of the two statistics “eoc” (end of minimal chain) and “pom” (parent of maximum leaf) on the set of secant trees. Their joint distribution restricted to the set {eoc-pom ≤ 1} is shown to satisfy two partial difference equation systems, to be symmetric and to be expressed in the form of an explicit three-variable generating function.
Second order strong divisibility sequences in an algebraic number field
Semigroup structures on ßN.