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On the Schertz conjecture
Ja Kyung Koo, Dong Sung Yoon
Schertz conjectured that every finite abelian extension of imaginary quadratic fields can be generated by the norm of the Siegel-Ramachandra invariants. We shall present a conditio…
Normal bases for modular function fields
Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon
We provide a concrete example of a normal basis for a finite Galois extension which is not abelian. More precisely, let be the field of meromorphic functions on…
On a problem of Hasse and Ramachandra
Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon
Let be an imaginary quadratic field, and let be a nontrivial integral ideal of . Hasse and Ramachandra asked whether the ray class field of modulo $\mathf…
Generators of Siegel modular function field of higher genus and level
Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon
For positive integers and , let be the field of meromorphic Siegel modular functions of genus and level whose Fourier coefficients belong to the t…
Siegel families with application to class fields
Ja Kyung Koo, Dong Hwa Shin, Dong Sung Yoon
We investigate certain families of meromorphic Siegel modular functions on which Galois groups act in a natural way. By using Shimura's reciprocity law we construct some algebraic…