Algebraic integers as values of elliptic functions
Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values
We present asymptotic representations for certain reciprocal sums of Fibonacci numbers and of Lucas numbers as a parameter tends to a critical value. As limiting cases of our results, we obtain Euler’s formulas for values of zeta functions.
Criteria for complex multiplication and transcendence properties of automorphic functions.
Diagonalization and rationalization of algebraic Laurent series
We prove a quantitative version of a result of Furstenberg [20] and Deligne [14] stating that the diagonal of a multivariate algebraic power series with coefficients in a field of positive characteristic is algebraic. As a consequence, we obtain that for every prime the reduction modulo of the diagonal of a multivariate algebraic power series with integer coefficients is an algebraic power series of degree at most and height at most , where is an effective constant that only depends on...
D'une mesure d'approximation simultanee a une mesure d'irrationalite: le cas de Γ(1/4) et Γ(1/3)
Formes linéaires de logarithmes de points algébriques sur une courbe elliptique de type
Nous obtenons une minoration d’une forme linéaire de logarithmes elliptiques de points algébriques d’une courbe elliptique à multiplication complexe définie sur . Cette minoration est optimale (à constante près) en la hauteur de la forme linéaire considérée.
Linear Forms in the Periods of the Exponential and Elliptic Functions.
Mesures d'approximation de valeurs de fonctions analytiques
Minorations de formes linéaires de logarithmes elliptiques
Quantitative results of algebraic independence and Baker's method
Some results on algebraic independence. (Quelques résultats d'indépendance algébrique.)
Specialization of endomorphism rings of abelian varieties
Sur la nature arithmétique des valeurs de fonctions modulaires
О приближении чисел, связанных с эллиптическими функциями Вейерштрасса.