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On the monodromy group of a second order linear differential equation. (Russian) Zbl 0615.34003

The equation under consideration is of the form \[ (1-z^ 2)w''+p(z)w'+(\lambda q(z)+r(z)/1-z^ 2))w=0, \] where p(z), q(z), r(z) are analytic in a connected domain \(D\subset {\mathbb{C}}\), containing \(I=[- 1,1]\). The author announces several results on the existence of a single- valued solution w in \(D\setminus I\) depending on the arithmetic properties of the characteristic exponents.
Reviewer: V.A.Tkačenko

MSC:

34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms
34A30 Linear ordinary differential equations and systems
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