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Package de.jtem.riemann.schottky

This package implements the numerical methods and algorithms for the evaluation of certain automorphic functions and forms in the context of Schottky uniformization.

See: Description

Package de.jtem.riemann.schottky Description

This package implements the numerical methods and algorithms for the evaluation of certain automorphic functions and forms in the context of Schottky uniformization. A classical theorem states that for any Riemann surface R  exists a Schottky group G such that  is conformally equivalent to the quotient W/G, where W denotes the set of discontinuity of G. A Schottky group is a free, finitely generated, discontinuous group that is purely loxodromic, i.e., a Schottky group of rank N, which equals the genus of the associated Riemann surface, can always be generated by N loxodromic transformations s1,...,sN. Further a loxodromic transformation si can be defined by its fixed points Ai and Bi and the loxodromic factor mi, with |mi|<1.

Thus all Schottky groups of rank N can be associated to a list of 3N complex values

S = { A1, B1, m1, ... , AN, BN, mN }

which is called the Schottky data.

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