Équations différentielles linéaires et majorations de multiplicités

DOI10.24033/asens.1488zbMath0578.12016OpenAlexW2600918066MaRDI QIDQ3699808

Frits Beukers, Daniel Bertrand

Publication date: 1985

Published in: Annales scientifiques de l'École normale supérieure (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=ASENS_1985_4_18_1_181_0

zbMATH Keywords

Fuchsian differential equationexponentsirregular singularitieslinear differential systemShidlovsky's lemma

Mathematics Subject Classification ID

Linear differential equations in abstract spaces (34G10) Abstract differential equations (12H20)

Related Items (16)

An algorithm for computing invariants of differential Galois groups ⋮ Effective estimates for global relations on Euler-type series ⋮ Testing reducibility of linear differential operators: A group theoretic perspective ⋮ Logarithms of algebraic numbers ⋮ Effective algebraic independence of values of \(E\)-functions ⋮ Values of \(E\)-functions are not Liouville numbers ⋮ Minimization of differential equations and algebraic values of 𝐸-functions ⋮ Rational approximation to values of \(G\)-functions, and their expansions in integer bases ⋮ Local zero estimates and effective division in rings of algebraic power series ⋮ Irrationality of values of L‐functions of Dirichlet characters ⋮ On 3-dimensional lattice walks confined to the positive octant ⋮ Siegel-Shidlovskii method in \(p\)-adic domain ⋮ Linear independence of values of \(G\)-functions. II: Outside the disk of convergence ⋮ SHIDLOVSKY’S MULTIPLICITY ESTIMATE AND IRRATIONALITY OF ZETA VALUES ⋮ Explicit degree bounds for right factors of linear differential operators ⋮ Hrushovski's algorithm for computing the Galois group of a linear differential equation

Cites Work

• Nearly perfect systems and effective generalizations of Shidlovski's theorem
• Differential modules and singular points of p-adic differential equations
• Jordan decomposition for a class of singular differential operators
• Algebraic matric groups and the Picard-Vessiot theory of homogeneous linear ordinary differential equations
• A conjecture in the arithmetic theory of differential equations
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