Some applications of eta-quotients

Ick Sun Eum, Ja Kyung Koo, Dong Hwa Shin

Published 2014-01-17Version 1

We show that every modular form on $\Gamma_0(2^n)$ ($n\geq2$) can be expressed as a sum of eta-quotients. Furthermore, we construct a primitive generator of the ring class field of the order of conductor $4N$ ($N\geq1$) in an imaginary quadratic field in view of the special value of certain eta-quotient.