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
A Note on Class Numbers of the Simplest Cubic Fields
β Scribed by Dongho Byeon
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 232 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
For a prime number l, let h> J be the class number of the maximal real subfield of the l-th cyclotomic field. For each natural number N, it is plausible but not yet proved that there exist infinitely many prime numbers l with h> J 'N. We prove an analogous assertion for cyclotomic function fields.
## Abstract Is it possible to give an abstract characterisation of constructive real numbers? A condition should be that all axioms are valid for Dedekind reals in any topos, or for constructive reals in Bishop mathematics. We present here a possible firstβorder axiomatisation of real numbers, whic
Let q be a power of a prime number p and k=F q (T ) the rational function field with a fixed indeterminate T. For an irreducible monic P=P(T ) in R=F q [T], let k(P) + be the maximal real subfield of the P th cyclotomic function field and h + T (P) the class number of k(P) + associated to R. We prov