An automorphic function 
of a complex variable
is one which is analytic (except for poles) in a domain
and which is invariant under a countably infinite
group of linear fractional transformations
(also known as Möbius transformations)
Automorphic functions are generalizations of trigonometric
functions and elliptic functions.
See also
Automorphic Form,
Modular Function,
Möbius Transformations,
Zeta Fuchsian
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References
Ford, L. Automorphic Functions. New York: McGraw-Hill, 1929.Hadamard, J.; Gray, J. J.;
and Shenitzer, A. Non-Euclidean
Geometry in the Theory of Automorphic Forms. Providence, RI: Amer. Math.
Soc., 1999.Shimura, G. Introduction
to the Arithmetic Theory of Automorphic Functions. Princeton, NJ: Princeton
University Press, 1971.Siegel, C. L. Topics
in Complex Function Theory, Vol. 2: Automorphic Functions and Abelian Integrals.
New York: Wiley, 1988.Referenced on Wolfram|Alpha
Automorphic Function
Cite this as:
Weisstein, Eric W. "Automorphic Function."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AutomorphicFunction.html
Subject classifications
