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Mathematics of Computation

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On computations with dessins d'enfants


Authors: Ali Kamalinejad and Mehrdad Shahshahani
Journal: Math. Comp. 86 (2017), 419-436
MSC (2010): Primary 11G32, 14H30, 14H52, 14H57, 14Q05
DOI: https://doi.org/10.1090/mcom/3110
Published electronically: April 19, 2016
MathSciNet review: 3557805
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Abstract: The geometric theory of dessins d'enfants is used to make explicit calculations on curves. In particular, an algorithmic procedure for the construction of ramified covering of curves over number fields with prescribed ramifications and for the explicit construction of Jenkins-Strebel differentials are developed.


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Additional Information

Ali Kamalinejad
Affiliation: School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
Email: kamalinejad@ipm.ir

Mehrdad Shahshahani
Affiliation: Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran
Email: mshahshahani@gmail.com

DOI: https://doi.org/10.1090/mcom/3110
Received by editor(s): May 17, 2014
Received by editor(s) in revised form: February 27, 2015, and June 9, 2015
Published electronically: April 19, 2016
Additional Notes: The second author was partially supported by the NSF grant DMS-128775 at Stanford University
Article copyright: © Copyright 2016 American Mathematical Society