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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


A Note on the Divisibility of Class Numb
✍ Gang Yu 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 118 KB

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

Class Numbers of Real Quadratic Function
✍ Humio Ichimura 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 160 KB

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

Divisibility by 2-Powers of Certain Quad
✍ P. Stevenhagen 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 726 KB

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