Variation of the argument of the Riemann ξ function on vertical lines
Variation of the number of lattice points in large balls
Variation of the reduction type of elliptic curves under small base change with wild ramification
We study the variation of the reduction type of elliptic curves under base change. A complete description of the variation is given when the base field is the p-adic field and the base change is of small degree.
Variation of the root number in families of elliptic curves
Variation on a theme of MacDonald.
Variationen über ein diophantisches Thema.
Variations on a question concerning the degrees of divisors of
In this paper, we examine a natural question concerning the divisors of the polynomial : “How often does have a divisor of every degree between and ?” In a previous paper, we considered the situation when is factored in . In this paper, we replace with , where is an arbitrary-but-fixed prime. We also consider those where this condition holds for all .
Variations on a theme of rationality of cycles
We prove certain weak versions of some celebrated results due to Alexander Vishik comparing rationality of algebraic cycles over the function field of a quadric and over the base field. The original proofs use Vishik’s symmetric operations in the algebraic cobordism theory and work only in characteristic 0. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2. Our weak versions are still sufficient for existing applications. In particular, Vishik’s...
Variations on a theme of Runge: effective determination of integral points on certain varieties
We consider some variations on the classical method of Runge for effectively determining integral points on certain curves. We first prove a version of Runge’s theorem valid for higher-dimensional varieties, generalizing a uniform version of Runge’s theorem due to Bombieri. We then take up the study of how Runge’s method may be expanded by taking advantage of certain coverings. We prove both a result for arbitrary curves and a more explicit result for superelliptic curves. As an application of our...
Variations on a theme of Sierpiński.
Variations on Euclid's formula for perfect numbers.
Variations sur un thème de Carl Runge
Variations sur un thème de Mahler.
Variations sur un thème de Siegel et Hecke
Variations sur un thème de Siegel-Hecke.
Variations sur un thème de Siegel-Hecke
Variétés abéliennes et indépendance albébrique II: Un analogue abélien du théorème de Lindeman-Weierstraß.
Variétés abéliennes et indépendance algébrique. I.
Variétés abéliennes et invariants arithmétiques
Dans la continuité de nos travaux précédents, nous étudions un analogue, pour le modèle de Néron d’une variété abélienne semi-stable sur un corps de nombres, du class-invariant homomorphism introduit par M. J. Taylor, qui nous permet de mesurer la structure galoisienne de certains torseurs.
Variétés de Drinfeld compactes