Real quadratic fields with class numbers divisible by n
✍ Scribed by P.J Weinberger
- Publisher
- Elsevier Science
- Year
- 1973
- Tongue
- English
- Weight
- 184 KB
- Volume
- 5
- Category
- Article
- ISSN
- 0022-314X
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📜 SIMILAR VOLUMES
Suppose g > 2 is an odd integer. For real number X > 2, define S g ðX Þ the number of squarefree integers d4X with the class number of the real quadratic field Qð ffiffiffi d p Þ being divisible by g. By constructing the discriminants based on the work of Yamamoto, we prove that a lower bound S g ðX
For a prime number p, let ކ p be the finite field of cardinality p and X ϭ X p a fixed indeterminate. We prove that for any natural number N, there exist infinitely many pairs ( p, K/ކ p (X )) of a prime number p and a ''real'' quadratic extension K/ކ p (X ) for which the genus of K is one and
We study the divisibility of the strict class numbers of the quadratic fields of discriminant \(8 p,-8 p\), and \(-4 p\) by powers of 2 for \(p \equiv 1 \bmod 4\) a prime number. Various criteria for divisibility by 8 are discussed, and an analogue of the relation \(8\left|h_{x_{p}} \Leftrightarrow