A methodic approach to the transcendence and algebraic independence of values of analytic functions

DOI10.1006/jnth.1997.2130zbMath0901.11026OpenAlexW1988529985MaRDI QIDQ1358802

Patrice Philippon

Publication date: 23 June 1997

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1997.2130

zbMATH Keywords

algebraic independencealgebraic approximationsvalues of analytic functionstranscendence of \(\pi\)interpolation determinantsexponential function of a Drinfeld modulenon-maximality of the rank of a matrix

Mathematics Subject Classification ID

Algebraic independence; Gel'fond's method (11J85) Transcendence (general theory) (11J81)

Related Items (12)

APPROXIMATIONS FONCTIONNELLES DES COURBES DES ESPACES PROJECTIFS ⋮ Multiplicity estimate for solutions of extended Ramanujan's system ⋮ Algebraic approximations of points in projective spaces. I ⋮ Approximation diophantienne et indépendance algébrique de logarithmes ⋮ ZERO ORDER ESTIMATES FOR ANALYTIC FUNCTIONS ⋮ The Schwarz lemma for Cartesian products ⋮ Auxiliary functions in transcendental number theory ⋮ New results on algebraic independence with Mahler's method ⋮ Transcendence and modular functions ⋮ Elliptic Functions and Transcendence ⋮ Sur l'approximation algébrique en degré de transcendance un. (On algebraic approximation in transcendence degree one) ⋮ Approximation by algebraic numbers

Cites Work

• Une mesure d'indépendance algébrique. (A measure of algebraic independence)
• Grands degrés de transcendance pour des familles d'exponentielles. (Large transcendence degrees for families of exponentials)
• Simultaneous approximation and algebraic independence
• Diophantine approximation
• Abelian varieties and algebraic independence. I
• Théorème de Baker et modules de Drinfeld. (Baker's theorem and Drinfeld modules)
• Gelfond's theorem for Drinfeld modules
• New zero lemmas in commutative algebraic groups
• Algebraic independence and products of Drinfeld modules
• Algebraic independence criteria.
• New aspects of transcendence
• A proof of the Mahler-Manin conjecture
• Multiplicity lemmas and \(T\)-modules
• Algebraic approximations of points in projective spaces. I
• Valeurs algébriques de fonctions analytiques
• Approximation algébrique de nombres lies aux fonctions elliptiques et exponentielle
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