Counting integral Lamé equations by means of dessins d'enfants

Author:
Sander R. Dahmen

Journal:
Trans. Amer. Math. Soc. **359** (2007), 909-922

MSC (2000):
Primary 34L40, 34M15; Secondary 11F11, 14H30

Published electronically:
September 12, 2006

MathSciNet review:
2255201

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Abstract | References | Similar Articles | Additional Information

Abstract: We obtain an explicit formula for the number of Lamé equations (modulo linear changes of variable) with index and projective monodromy group of order , for given and . This is done by performing the combinatorics of the `dessins d'enfants' associated to the Belyi covers which transform hypergeometric equations into Lamé equations by pull-back.

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Additional Information

**Sander R. Dahmen**

Affiliation:
Department of Mathematics, Utrecht University, Budapestlaan 6, 3584 CD Utrecht, The Netherlands

Email:
dahmen@math.uu.nl

DOI:
http://dx.doi.org/10.1090/S0002-9947-06-03924-9

Keywords:
Lam\'{e} equation,
algebraic solution,
monodromy,
dessin d'enfants

Received by editor(s):
June 25, 2004

Received by editor(s) in revised form:
January 21, 2005

Published electronically:
September 12, 2006

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.