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Divisibility by 2-Powers of Certain Quadratic Class Numbers

โœ Scribed by P. Stevenhagen

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
726 KB
Volume
43
Category
Article
ISSN
0022-314X

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โœฆ Synopsis

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 8\right| h_{k_{j}}) and (8 \mid h_{4}) is given for divisibility by 16 . We present numerical dala related to the known and conjectured densities of primes (p) giving rise to specific 2-power divisibilities. ' 1943 Academic Press, Inc.

๐Ÿ“œ SIMILAR VOLUMES

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