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
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
