Geodesic
On the Divisibility of the Class Numbers of Q(√−p) and Q(√−2p) by 16.
Canadian mathematical bulletin, Tome 25 (1982) no. 2, pp. 200-206

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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.
DOI : 10.4153/CMB-1982-027-0
Mots-clés : 12A25, 12A50, Key words, and phrases, class number, imaginary quadratic field, binary quadratic forms 
Leonard, Philip A.; Williams, Kenneth S. On the Divisibility of the Class Numbers of Q(√−p) and Q(√−2p) by 16.. Canadian mathematical bulletin, Tome 25 (1982) no. 2, pp. 200-206. doi: 10.4153/CMB-1982-027-0
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[1] 1. Bauer, Helmut, Zur Berechnung der 2-Klassenzahl der quadratische Zahlkörper mit genau zwei verschiedenen Diskriminantenprimteilem, J. Reine Angew. Math. 248 (1971), 42-46. Google Scholar

[2] 2. Berndt, Bruce C., Classical theorems on quadratic residues, L'Enseignement Math. 22 (1976), 261-304. Google Scholar

[3] 3. Brown, Ezra, The class number of Q(√-p), for p ≡ 1 (mod 8) a prime, Proc. Amer. Math. Soc. 31 (1972), 381-383. Google Scholar

[4] 4. Brown, Ezra, The power of 2 dividing the class-number of a binary quadratic discriminant, J. Number Theory 5 (1973), 413-419. Google Scholar

[5] 5. Brown, Ezra, Class numbers of quadratic fields, Symp. Mat. 15 (1975), 403-411. Google Scholar

[6] 6. Hasse, Helmut, Ober die Klassenzahl des Körpers P(√-p) mit einer Primzahl p ≡ 1 (mod 23), Aequationes Math. 3 (1969), 165-169. Google Scholar

[7] 7. Hasse, Helmut, Über die Klassenzahl des Körpers P(√-2p) mit einer Primzahl p ≠ 2, J. Number Theory 1 (1969), 231-234. Google Scholar

[8] 8. Hasse, Helmut, Über die Teilbarkeit durch 23 der Klassenzahl imaginär-quadratischer Zahlkörper mit genau zwei verschiedenen Diskriminantenprimteilem, J. Reine Angew. Math. 241 (1970), 1-6. Google Scholar

[9] 9. Kaplan, Pierre, Divisibilité par 8 du nombre des classes des corps quadratiques dont le 2-groupe des classes est cyclique, et réciprocité biquadratique, J. Math. Soc. Japan 25 (1973), 596-608. Google Scholar

[10] 10. Kaplan, Pierre, Cycles d'ordre au moins 16 dans le 2-groupe des classes d'idéaux de certains corps quadratiques, Bull. Soc. Math. France Mém. No. 49-50 (1977), 113-124. Google Scholar

[11] 11. Kaplan, Pierre and Williams, Kenneth S., On the class numbers of Q(√?2p) modulo 16, for p ≡ 1 (mod 8) a prime, Acta Arith. (to appear). Google Scholar

[12] 12. Williams, Kenneth S., On the class number of Q(√-p) modulo 16, for p ≡ 1 (mod 8) a prime, Acta Arith. (to appear). Google Scholar

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