✦ LIBER ✦

A Note on the Divisibility of Class Numbers of Real Quadratic Fields

✍ Scribed by Gang Yu

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 118 KB
Volume: 97
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2773

No coin nor oath required. For personal study only.

✦ Synopsis

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 Þ4X 1=gÀe holds for any fixed e > 0, which improves a result of Ram Murty.

📜 SIMILAR VOLUMES

Infinitely Many Real Quadratic Fields of

Infinitely Many Real Quadratic Fields of Class Number One

✍ T.A. Schmidt 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 110 KB

Class Numbers of Real Quadratic Function

Class Numbers of Real Quadratic Function Fields of Genus One

✍ 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

A Note on Class Numbers of the Simplest

A Note on Class Numbers of the Simplest Cubic Fields

✍ Dongho Byeon 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 232 KB

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.

Parametrization of the Quadratic Fields

Parametrization of the Quadratic Fields Whose Class Numbers are Divisible by Three

✍ Yasuhiro Kishi; Katsuya Miyake 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 132 KB

Class Number 1 Criteria for Real Quadrat

Class Number 1 Criteria for Real Quadratic Fields of Richaud–Degert Type

✍ Dongho Byeon; Hyun Kwang Kim 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 486 KB

In this paper we develop two ways of computing special values of zeta function attached to a real quadratic field. Comparing these values we obtain various class number 1 criteria for real quadratic fields of Richaud Degert type.

A note on the axiomatisation of real num

A note on the axiomatisation of real numbers

✍ Thierry Coquand; L. Henri Lombardi 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 86 KB 👁 2 views

## 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 first‐order axiomatisation of real numbers, whic