๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

The Maximal Unramified Extensions of the Imaginary Quadratic Number Fields with Class Number Two

โœ Scribed by Ken Yamamura


Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
290 KB
Volume
60
Category
Article
ISSN
0022-314X

No coin nor oath required. For personal study only.

โœฆ Synopsis


The maximal unramified extensions of the imaginary quadratic number fields with class number two are determined explicitly under the Generalized Riemann Hypothesis.


๐Ÿ“œ SIMILAR VOLUMES


Refined Lower Bounds on the 2-Class Numb
โœ Elliot Benjamin; Charles J. Parry ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 125 KB

Let k be an imaginary quadratic number field with C k, 2 , the 2-Sylow subgroup of its ideal class group, isomorphic to Zร‚2Z\_Zร‚2Z\_Zร‚2Z. By the use of various versions of the Kuroda class number formula, we improve significantly upon our previous lower bound for |C k 1 , 2 | , the 2-class number of

The Exponent 2-Class-Group Problem for N
โœ S. Louboutin ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 350 KB

Focusing on a particular case, we will show that one can explicitly determine the quartic fields \(\mathbf{K}\) that have ideal class groups of exponent \(\leqslant 2\), provided that \(\mathbf{K} / \mathbf{Q}\) is not normal, provided that \(\mathbf{K}\) is a quadratic extension of a fixed imaginar

A Note on the Divisibility of Class Numb
โœ Gang Yu ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 118 KB

Suppose g > 2 is an odd integer. For real number X > 2, define S g รฐX รž the number of squarefree integers d4X with the class number of the real quadratic field Qรฐ ffiffiffi d p รž being divisible by g. By constructing the discriminants based on the work of Yamamoto, we prove that a lower bound S g รฐX

On the Class Numbers of the Maximal Real
โœ Humio Ichimura ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 275 KB

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.

On the Class Numbers of the Maximal Real
โœ Humio Ichimura ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 229 KB

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