The relative class numbers of certain imaginary abelian number fields and determinants
✍ Scribed by Akira Endô
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 299 KB
- Volume
- 34
- Category
- Article
- ISSN
- 0022-314X
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📜 SIMILAR VOLUMES
We construct a generalization of Demjanenko's matrix for an arbitrary imaginary abelian field and prove a relation formula between the determinant of this matrix and the relative class number. In a special case, we prove that the determinant of this matrix coincides with Maillet's determinant. As an
Let p be an odd regular prime number. We prove that there exist infinitely many totally real number fields k of degree p&1 whose class numbers are not divisible by p. Moreover, for certain regular prime number p, we prove that there exist infinitely many totally real number fields k of degree p&1 wh
The maximal unramified extensions of the imaginary quadratic number fields with class number two are determined explicitly under the Generalized Riemann Hypothesis.