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On the Parity of the Class Number of a Biquadratic Field

โœ Scribed by R. Kucera

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
271 KB
Volume
52
Category
Article
ISSN
0022-314X

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๐Ÿ“œ SIMILAR VOLUMES

On the Parity of the Class Number of the
On the Parity of the Class Number of the Field Q(p,q,r)
โœ Michal Bulant ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 406 KB

If ( pร‚q)=( pร‚r)=(qร‚r)=&1, fix u pq , u pr , u qr # Z satisfying u 2 pq #pq (mod r), u 2 pr #pr (mod q), u 2 qr #qr (mod p). Then h is even if and only if (u pq ร‚r)(u pr ร‚q)(u qr ร‚p)=&1. 2. If ( pร‚q)=1, ( pร‚r)=(qร‚r)=&1, then the parity of h is the same as the parity of the class number of the biqua

A Note on Class Numbers of the Simplest
A Note on Class Numbers of the Simplest Cubic Fields
โœ Dongho Byeon ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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.

A Note on the Divisibility of Class Numb
A Note on the Divisibility of Class Numbers of Real Quadratic Fields
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
On the Class Numbers of the Maximal Real Subfields of Cyclotomic Function Fields
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.

Refined Lower Bounds on the 2-Class Numb
Refined Lower Bounds on the 2-Class Number of the Hilbert 2-Class Field of Imaginary Quadratic Number Fields with Elementary 2-Class Group of Rank 3
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