Ick Sun Eum

Some applications of modular units

We show that a weakly holomorphic modular function can be written as a sum of modular units of higher level. We further find a necessary and sufficient condition for a Siegel modular function of degree

On some applications of Eisenstein series

g

Some applications of eta-quotients

to have neither zero nor pole on the domain when restricted to certain subset of the Siegel upper half-space

Ring class invariants over imaginary quadratic fields

\mathbb{H}_g

Primitive generators of certain class fields

.

Representations by x12+2x22+x32+x42+x1x3+x1x4+x2x4

We derive the uniqueness of the theta functions associated with certain quadratic forms. Furthermore, we show some partially multiplicative relations between the representation numbers of such quadratic forms. To this end we apply Fricke involutions and Hecke operators to Eisenstein series.

A modularity criterion for Klein forms, with an application to modular forms of level 13

We show that every modular form on

On some modularity of Klein forms

\Gamma_0(2^n)

On some extension of Gauss' work and applications (II).

(

Representations by some quinary quadratic forms of level 8

n\geq2