On a Parameterized Family of Quadratic and Cubic Fields
β Scribed by D.A. Buell; V. Ennola
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 492 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0022-314X
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π SIMILAR VOLUMES
Let Do0 be the fundamental discriminant of an imaginary quadratic field, and hΓ°DΓ its class number. In this paper, we show that for any prime p > 3 and e ΒΌ Γ1; 0; or 1, ] ΓX oDo0 j hΓ°DΓc0 Γ°mod pΓ and D p ΒΌ e 4 p ffiffiffiffi X p log X :
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