Abstract
We introduce the primitivity of Fricke families, and give some examples. As its application, we first construct generators of the function field of the modular curve of level N in terms of Fricke functions and Siegel functions, respectively. Furthermore, we use the special values of a certain function in a totally primitive Fricke family of level N in order to generate ray class fields of imaginary quadratic fields.
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The first named author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (2016R1A5A1008055). The third named (corresponding) author was supported by Hankuk University of Foreign Studies Research Fund of 2016.
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Jung, H.Y., Koo, J.K. & Shin, D.H. Primitive and Totally Primitive Fricke Families with Applications. Results Math 71, 841–858 (2017). https://doi.org/10.1007/s00025-016-0585-0
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DOI: https://doi.org/10.1007/s00025-016-0585-0