This study shows minimal polynomials of eta-quotients evaluated at CM points, suggesting connections to ring class fields.
We study certain eta-quotients of weight zero evaluated at CM points of imaginary quadratic orders. Using the theory of extended form class groups, we show that these special values generate the corresponding ring class fields and we provide explicit descriptions of their minimal polynomials. Finally, we apply these results to certain Diophantine problems.
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Ho Yun Jung (2025) studied this question.
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