SU\G(𝔸)/K·U

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

Philip Leonard, Kenneth S. Williams

Type: Article

Publication Date: 1982-06-01

Citations: 19

DOI: https://doi.org/10.4153/cmb-1982-027-0

Abstract

Abstract 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 = −2 p , where p is a prime congruent to ±1 modulo 8.

Locations

  • Canadian Mathematical Bulletin - View - PDF

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+ Classical theorems on quadratic residues 1976 Bruce C. Berndt
+ The power of 2 dividing the class-number of a binary quadratic discriminant 1973 Ezra Brown
+ The Class Number of Q(√- p), for p ≡1 (mod 8) A Prime 1972 Ezra Brown
+ Über die Klassenzahl des Körpers P(√−2p) mit einer Primzahl p ≠ 2 1969 Helmut Hasse
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