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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Counting integral Lamé equations by means of dessins d’enfants
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by Sander R. Dahmen PDF
Trans. Amer. Math. Soc. 359 (2007), 909-922 Request permission

Abstract:

We obtain an explicit formula for the number of Lamé equations (modulo linear changes of variable) with index $n$ and projective monodromy group of order $2N$, for given $n \in \mathbb {Z}$ and $N \in \mathbb {N}$. 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
  • Received by editor(s): June 25, 2004
  • Received by editor(s) in revised form: January 21, 2005
  • Published electronically: September 12, 2006
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 909-922
  • MSC (2000): Primary 34L40, 34M15; Secondary 11F11, 14H30
  • DOI: https://doi.org/10.1090/S0002-9947-06-03924-9
  • MathSciNet review: 2255201