Automorphic Function

An automorphic function f(z) of a complex variable z is one which is analytic (except for poles) in a domain D 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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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.

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Automorphic Function

Cite this as:

Weisstein, Eric W. "Automorphic Function." From MathWorld--A Wolfram Web Resource.

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