This article is cited in 2 papers

On the 65th birthday of R.Cushman

Unitary Monodromy of Lamé Differential Operators

F. Beukers

Mathematics Institute, University of Utrecht, P.O. Box 80.010, 3508 TA Utrecht, The Netherlands

Abstract: The classical second order Lamé equation contains a so-called accessory parameter $B$. In this paper we study for which values of $B$ the Lamé equation has a monodromy group which is conjugate to a subgroup of $SL(2,\mathbb{R})$ (unitary monodromy with indefinite hermitian form). We reformulate the problem as a spectral problem and give an asymptotic expansion for the spectrum.

Keywords: unitary monodromy, Lamé differential equation.

MSC: 34M35, 33E10

Received: 04.06.2007
Accepted: 09.09.2007

Language: English

DOI: 10.1134/S1560354707060068

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