DETERMINATION OF THE FRICKE FAMILIES

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 ${\math...

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Bibliographic Details
Published inJournal of the Korean Mathematical Society Vol. 53; no. 6; pp. 1445 - 1457
Main Authors Eum, Ick Sun, Shin, Dong Hwa
Format Journal Article
LanguageKorean
Published 2016
Subjects
Fricke families
modular units
modular functions
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Summary: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.
Bibliography:KISTI1.1003/JNL.JAKO201634347321235
ISSN:0304-9914