Jacobi theta functions can be used to uniformize all elliptic curves. Jacobi elliptic functions may also be used to uniformize some hyperelliptic curves, although only two such examples are known. The classical example is the Burnside curve, and the second was found by Farkas-Kra around 1995.
Uniformization
See also
Burnside Curve, Universal Cover, Uniformization TheoremReferences
Brezhnev, Yu. V. "Uniformisation: On the Burnside Curve
."
9 Dec 2001. http://arxiv.org/abs/math.CA/0111150.Brezhnev,
Yu. V. "On Uniformization of Algebraic Curves." Mosc. Math. J. 8,
233-271, 2008.Ford, L. Automorphic
Functions. New York: McGraw-Hill, 1929.Referenced on Wolfram|Alpha
UniformizationCite this as:
Weisstein, Eric W. "Uniformization." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Uniformization.html