Ja Kyung Koo

On holomorphic differentials of some algebraic function field of one variable over C

We give holomorphic differentials of some algebraic function field K of complex dimension one which is a generalisation of a hyperelliptic field.

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 Fricke families and application to the Lang–Schertz conjecture

g

On some arithmetic properties of Siegel functions (II)

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

p-adic interpolating function associated with Euler numbers

\mathbb{H}_g

On some applications of Eisenstein series

.

Algebraic integers as special values of modular units

We first investigate two kinds of Fricke families consisting of Fricke functions and Siegel functions, respectively. And, in terms of their special values we generate ray class fields of imaginary quadratic fields, which is related to the Lang-Schertz conjecture.

On the infinite products derived from theta series II

Abstract. Let K be an imaginary quadratic field of discriminant . We deal with problems of constructing normal bases between abelian extensions of K by making use of singular values of Siegel functions. First, we find normal bases of ring class fields of orders of bounded conductors depending on dK over K by using a criterion deduced from the Frobenius determinant relation. Next, denoting by the ray class field modulo N of K for an integer we consider the field extension for a prime and a positive integer m relatively prime to p and then find normal bases of all intermediate fields over by utilizing Kawamotos arguments. We further investigate certain Galois module structure of the field extension with , which would be an extension of Komatsus work.

Siegel families with application to class fields

Abstract In this paper, we investigate some relations between Bernoulli numbers and Frobenius-Euler numbers, and we study the values for p-adic l-function.

Generation of ring class fields by eta-quotients

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.