Algebraic solutions of linear differential equations: an arithmetic approach
CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
CARUSO, Xavier
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]
Language
en
Document de travail - Pré-publication
This item was published in
2023-04-11
English Abstract
Given a linear differential equation with coefficients in $\mathbb{Q}(x)$, an important question is to know whether its full space of solutions consists of algebraic functions, or at least if one of its specific solutions ...Read more >
Given a linear differential equation with coefficients in $\mathbb{Q}(x)$, an important question is to know whether its full space of solutions consists of algebraic functions, or at least if one of its specific solutions is algebraic.After presenting motivating examples coming from various branches of mathematics, we advertise in an elementary way a beautiful local-global arithmetic approach to these questions, initiated by Grothendieck in the late sixties.This approach has deep ramifications and leads to the still unsolved Grothendieck-Katz $p$-curvature conjecture.Read less <
ANR Project
Correspondance de Langlands p-adique : une approche constructive et algorithmique - ANR-18-CE40-0026
Décider l'irrationalité et la transcendance - ANR-19-CE40-0018
Algorithmes Efficaces pour Guessing, Inégalités, Sommation - ANR-22-CE91-0007
Décider l'irrationalité et la transcendance - ANR-19-CE40-0018
Algorithmes Efficaces pour Guessing, Inégalités, Sommation - ANR-22-CE91-0007
Origin
Hal imported