Fundamental domains of Dirichlet functions. (English) Zbl 1417.30004

Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 20th international conference on geometry, integrability and quantization, Sts. Constantine and Elena (near Varna), Bulgaria, June 2–7, 2018. Sofia: Avangard Prima; Sofia: Bulgarian Academy of Sciences, Institute of Biophysics and Biomedical Engineering. Geom. Integrability Quantization 20, 131-1160 (2019).
Summary: The concept of fundamental domain, as defined by Ahlfors, plays an important role in the study of different classes of analytic functions. For more than a century the Dirichlet functions have been intensely studied by mathematicians working in the field of number theory as well as by those interested in their analytic properties. The fundamental domains pertain to the last field, yet we found a lot of theoretic aspects which can be dealt with by knowing in detail those domains. We gathered together in this survey paper some recent advances in this field. Proofs are provided for some of the theorems, so that the reader can navigate easily through it.
For the entire collection see [Zbl 1408.53003].


30B50 Dirichlet series, exponential series and other series in one complex variable
30C35 General theory of conformal mappings
30-02 Research exposition (monographs, survey articles) pertaining to functions of a complex variable
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