Abstract
This article studies the Riemann surfaces generated by factorization of the multiplicative group of nonzero complex numbers through its discrete subgroups. The first section of the article provides a classification of the discrete subgroups of (,·), and the Riemann surfaces that they generate. Meromorphic functions on these surfaces correspond to functions that are multiplicative-periodic in the complex plane and have essential singularities at 0 and ∞. The second part of the article presents constructions of multiplicative-periodic functions. The final section discusses the relationship between the functions constructed and elliptic double periodic functions.
Published Version
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