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Generalization of Kummer's criterion for divisibility of class numbers

โœ Scribed by Norio Adachi

Publisher
Elsevier Science
Year
1973
Tongue
English
Weight
473 KB
Volume
5
Category
Article
ISSN
0022-314X

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๐Ÿ“œ SIMILAR VOLUMES

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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

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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