A note on the splitting of the Hilbert class field
β Scribed by Gary Cornell; Michael Rosen
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 340 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let k be an algebraic number field. We describe a procedure for computing the Hilbert class field 1(k) of k, i.e., the maximal abelian extension unramified at all places. In the first part of the paper we outline the underlying theory and in the second part we present the important algorithms and gi
In this note, it is shown that the HardyαHilbert inequality for double series can Ε½ . be improved by introducing a proper weight function of the form rsin rp y Ε½ . 1y1rr Ε½ Ε½ . . O n rn with O n ) 0 into either of the two single summations. When r r r s 2, the classical Hilbert inequality is improved
In this note, we extend the Uchida Washington construction of the simplest cubic fields with class numbers divisible by a given rational integer, to the wildly ramified case, which was previously excluded.
Suppose g > 2 is an odd integer. For real number X > 2, define S g Γ°X Γ the number of squarefree integers d4X with the class number of the real quadratic field QΓ° ffiffiffi d p Γ being divisible by g. By constructing the discriminants based on the work of Yamamoto, we prove that a lower bound S g Γ°X