Geodesic
Accessory Parameters for Four-Punctured Spheres
Symmetry, integrability and geometry: methods and applications, Tome 18 (2022) Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the accessory parameter problem for four-punctured spheres from the point of view of modular forms. The value of the accessory parameter giving the uniformization is characterized as the unique zero of a system of equations. This gives an effective method to compute the uniformizing differential equation. As an application, we compute numerically and study the local expansion of the real-analytic function associating to a four-punctured sphere the value of its uniformizing parameter, and make some observations on its coefficients.
Keywords: accessory parameters, Fuchsian uniformization, modular forms. 
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     author = {Gabriele Bogo},
     title = {Accessory {Parameters} for {Four-Punctured} {Spheres}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a23/}
}
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Gabriele Bogo. Accessory Parameters for Four-Punctured Spheres. Symmetry, integrability and geometry: methods and applications, Tome 18 (2022). http://geodesic.mathdoc.fr/item/SIGMA_2022_18_a23/

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