Distribution of rational points on the real line

Distribution of Rational Points: A Survey

distribution of rational points: a survey

Distribution of Rational Points: a Survey

In this survey we discuss Manin’s conjectures about the distribution of rational points on certain classes of algebraic varieties.

Line Bundles, Rational Points and Ideal Classes

In this note, we will use the term “arithmetic variety” for a normal scheme X for which the structure morphism f : X → Spec(Z) is proper and flat. Let V be a proper, normal (not necessarily geometrically connected) variety over Q. Let us choose a normal model for V over Z, that is an arithmetic variety X whose generic fiber is identified with V . Suppose that F is a number field and consider th...

Orthogonal rational functions and quadrature on the real half line

In this paper we generalize the notion of orthogonal Laurent polynomials to orthogonal rational functions. Orthogonality is considered with respect to a measure on the positive real line. From this, Gauss-type quadrature formulas are derived and multipoint Padé approximants for the Stieltjes transform of the measure. Convergence of both the quadrature formula and the multipoint Padé approximant...