We present solutions for general theorems regarding algebraic independence of solutions of hypergeometric equation ensembles and the values of these solutions at algebraic points. The conditions of the theorems are necessary and sufficient. Furthermore, errors in theorems from F. Beukers and others are corrected
We give a combinatorial formula of the dimension of global solutions to a generalization of Gauss-Ao...
We provide a complete classification of the algebraicity of (generalized) hypergeometric functions w...
Anyone familiar with systems of polynomial equations (whether they majored in math or just had to so...
The paper is concerned with the transcendental numbers. The aim is to prove the algebraic independen...
The development of new methods for the algebraic property investigation of linear differential equat...
We obtain a necessary and sufficient condition for the linear independence of solutions of different...
We formulate and prove a combinatorial criterion to decide if an A-hypergeometric system of differen...
In 1955 A.B. Shidlovski's general theorems were published. They allow us to reduce the problem of al...
We explicitly give the relations between the hypergeometric solutions of the general hypergeometric ...
AbstractThe main theorem of this paper, proved using Mahler's method, gives a necessary and sufficie...
This work is a collaboration with B. Adamczewski (ICJ, France), T. Dreyfus (IRMA, France) and M. Wib...
In the frame of Mahler's method for algebraic independence we show that the algebraic relations over...
International audienceWe consider pairs of automorphisms (φ, σ) acting on fields of Laurent or Puise...
We obtain a necessary and sufficient condition for the linear independence of solutions of differen...
The study of hypergeometric functions started in 1813 with a paper by Gauss. Hypergeometric function...
We give a combinatorial formula of the dimension of global solutions to a generalization of Gauss-Ao...
We provide a complete classification of the algebraicity of (generalized) hypergeometric functions w...
Anyone familiar with systems of polynomial equations (whether they majored in math or just had to so...
The paper is concerned with the transcendental numbers. The aim is to prove the algebraic independen...
The development of new methods for the algebraic property investigation of linear differential equat...
We obtain a necessary and sufficient condition for the linear independence of solutions of different...
We formulate and prove a combinatorial criterion to decide if an A-hypergeometric system of differen...
In 1955 A.B. Shidlovski's general theorems were published. They allow us to reduce the problem of al...
We explicitly give the relations between the hypergeometric solutions of the general hypergeometric ...
AbstractThe main theorem of this paper, proved using Mahler's method, gives a necessary and sufficie...
This work is a collaboration with B. Adamczewski (ICJ, France), T. Dreyfus (IRMA, France) and M. Wib...
In the frame of Mahler's method for algebraic independence we show that the algebraic relations over...
International audienceWe consider pairs of automorphisms (φ, σ) acting on fields of Laurent or Puise...
We obtain a necessary and sufficient condition for the linear independence of solutions of differen...
The study of hypergeometric functions started in 1813 with a paper by Gauss. Hypergeometric function...
We give a combinatorial formula of the dimension of global solutions to a generalization of Gauss-Ao...
We provide a complete classification of the algebraicity of (generalized) hypergeometric functions w...
Anyone familiar with systems of polynomial equations (whether they majored in math or just had to so...
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