Some applications of eta-quotients

Ick Sun Eum; Ja Kyung Koo; Dong Hwa Shin

Some applications of eta-quotients

Number Theory 2014-01-20 v1

Authors: Ick Sun Eum , Ja Kyung Koo , Dong Hwa Shin

Abstract

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.

Keywords

eta-quotients modular forms ring class field imaginary quadratic field primitive generator

Cite

@article{arxiv.1401.4226,
  title  = {Some applications of eta-quotients},
  author = {Ick Sun Eum and Ja Kyung Koo and Dong Hwa Shin},
  journal= {arXiv preprint arXiv:1401.4226},
  year   = {2014}
}

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