A Banach space determined by the Weil height
A Bogomolov property for curves modulo algebraic subgroups
Generalizing a result of Bombieri, Masser, and Zannier we show that on a curve in the algebraic torus which is not contained in any proper coset only finitely many points are close to an algebraic subgroup of codimension at least . The notion of close is defined using the Weil height. We also deduce some cardinality bounds and further finiteness statements.
A dynamical interpretation of the global canonical height on an elliptic curve.
A “Hardy-Littlewood” approach to the -unit equation
A natural series for the natural logarithm.
A new record for the canonical height on an elliptic curve over .
A Note on heights in certain infinite extensions of
We study the behaviour of the absolute Weil height of algebraic numbers in certain infinite extensions of . In particular, we obtain a Northcott type property for infinite abelian extensions of finite exponent and also a Bogomolov type property for certain fields which are a -adic analog of totally real fields. Moreover, we obtain a non-archimedean analog of a uniform distribution theorem of Bilu in the archimedean case.
A quantitative version of Siegel's theorem: integral points on elliptic curves and Catalan curves.
A relative Dobrowolski lower bound over abelian extensions
Algebraic S-integers of fixed degree and bounded height
Let k be a number field and S a finite set of places of k containing the archimedean ones. We count the number of algebraic points of bounded height whose coordinates lie in the ring of S-integers of k. Moreover, we give an asymptotic formula for the number of S̅-integers of bounded height and fixed degree over k, where S̅ is the set of places of k̅ lying above the ones in S.
An equivalent of Kronecker's theorem for powers of an algebraic number and structure of linear recurrences of fixed length
Approximation diophantienne sur les variétés semi-abéliennes
Arithmetic Distance Functions and Height Fuctions in Diophantine Geometry.