Ring-theoretic properties of Iwasawa algebras: a survey.
Riordan arrays, orthogonal polynomials as moments, and Hankel transforms.
Rogers-Ramanujan identities: A century of progress from mathematics to physics.
Rogers-Ramanujan-Slater type identities.
Röhmel's equation for quadratic forms.
Root separation for reducible integer polynomials
We construct parametric families of (monic) reducible polynomials having two roots very close to each other.
Root separation for reducible monic quartics
Root Systems and Elliptic Curves
Root systems and Jacobi forms
Root systems and the Erdős-Szekeres Problem
Roots of increasing sequences.
Roots of multiplicative functions
Roots of unity in definite quaternion orders
A commutative order in a quaternion algebra is called selective if it embeds into some, but not all, of the maximal orders in the algebra. It is known that a given quadratic order over a number field can be selective in at most one indefinite quaternion algebra. Here we prove that the order generated by a cubic root of unity is selective for any definite quaternion algebra over the rationals with type number 3 or larger. The proof extends to a few other closely related orders.
Rosen fractions and Veech groups, an overly brief introduction
We give a very brief, but gentle, sketch of an introduction both to the Rosen continued fractions and to a geometric setting to which they are related, given in terms of Veech groups. We have kept the informal approach of the talk at the Numerations conference, aimed at an audience assumed to have heard of neither of the topics of the title.The Rosen continued fractions are a family of continued fraction algorithms, each gives expansions of real numbers in terms of elements of a corresponding algebraic...
Rosser's sieve
Rost projectors and Steenrod operations.
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 in the space of Split octonions.
Rotations sur les groupes, nombres algébriques, et substitutions
Roth's theorem on systems of linear forms in function fields