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On the Divisibility of the Class Numbers of Q(√−p) and Q(√−2p) by 16.

Published online by Cambridge University Press:  20 November 2018

Philip A. Leonard  and
Kenneth S. Williams
Philip A. Leonard
Affiliation:
Arizona State University, Tempe, Arizona, U.S.A. 82581
Kenneth S. Williams
Affiliation:
Carleton University Ottawa, Ontario, CanadaK1s 5b6
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Abstract

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Let h(m) denote the class number of the quadratic field Q(√m). In this paper necessary and sufficient conditions for h (m) to be divisible by 16 are determined when m = −p, where p is a prime congruent to 1 modulo 8, and when m = −2p, where p is a prime congruent to ±1 modulo 8.

Keywords

12A2512A50Key wordsand phrasesclass numberimaginary quadratic fieldbinary quadratic forms
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 25 , Issue 2 , 01 June 1982 , pp. 200 - 206
Copyright
Copyright © Canadian Mathematical Society 1982

References

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