Construction of class fields by ideal class transfer

Abstract

In this thesis we mainly focus on the generation of class fields over a number field by ideal transfer. In general, it is well-known to generate the class fields by making use of modular functions. However, if we use the ideal transfer from the ideal class group of K to that of L, we can determine whether L is a class field of K or not. For the cases [L:K]=2, 3 or 4 with K a quadratic field, we transfer the ideals and calculate by using the result of transference. In the cases of the degree 5, 6 or 7 of L over K, we give the results of the ideal transfer and show the condition of being a class field.