# Indices d'un operateur differentiel matriciel et applications

Source: [Indices d'un operateur differentiel matriciel et applications](<https://www.sota2.com/research/paper/68fa4cf11e209131ce9509ca>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T09:03:26.388Z

Authors: K. Betina

Published: 2005-04-20T10:26:08.000Z

## Abstract

In this paper, one determines the formal index and the polynomial index of a matrix linear differential operator P with coefficients in Mn(C\[x\]) and detAm(x) not identically zero. Then, one applies these results to give a new proof of a Bezivin-Robba theorem equivalent to the Lindemann-Wierstrass theorem, as to find sufficient conditions on the Riccati matrix differential equation Y' = A(x)+B(x)Y +Y C(x)Y with coefficients in Mn(C\[x\]) so that any meromorphic solution is rational and other sufficient conditions so that the general solution is algebraic.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/math/0504407>)

[PDF](<https://arxiv.org/pdf/math/0504407.pdf>)