Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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DETERMINATION OF THE FRICKE FAMILIES

  • Eum, Ick Sun (School of Mathematics Korea Institute for Advanced Study) ;
  • Shin, Dong Hwa (Department of Mathematics Hankuk University of Foreign Studies)
  • Received : 2015.09.22
  • Published : 2016.11.01
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Abstract

For a positive integer N divisible by 4, let ${\mathcal{O}}^1_N({\mathbb{Q}})$ be the ring of weakly holomorphic modular functions for the congruence subgroup ${\Gamma}^1(N)$ with rational Fourier coefficients. We present explicit generators of the ring ${\mathcal{O}}^1_N({\mathbb{Q}})$ over ${\mathbb{Q}}$ in terms of both Fricke functions and Siegel functions, from which we are able to classify all Fricke families of such level N.

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Acknowledgement

Supported by : National Research Foundation (NRF)

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