REMARKS ON THE DIVISIBILITY OF THE CLASS NUMBERS OF IMAGINARY QUADRATIC FIELDS
Glasgow mathematical journal, Tome 53 (2011) no. 2, pp. 379-389
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We consider the divisibility of the class numbers of imaginary quadratic fields , where q is an odd prime number, k and n are positive integers. Suppose that k ≡ 1 mod 2 or n ≢ 3 mod 6. We show that the class numbers of imaginary quadratic fields ≠ are divisible by n for q ≡ 3 mod 8. This is a generalization of the result of Kishi for imaginary quadratic fields when k ≡ 1 mod 2 or n ≢ 3 mod 6. We also show that the class numbers of imaginary quadratic fields ≠ are divisible by n for q ≡ 1 mod 4 and the class numbers of imaginary quadratic fields ≠ are divisible by n for q ≡ 7 mod 8.
ITO, AKIKO. REMARKS ON THE DIVISIBILITY OF THE CLASS NUMBERS OF IMAGINARY QUADRATIC FIELDS. Glasgow mathematical journal, Tome 53 (2011) no. 2, pp. 379-389. doi: 10.1017/S0017089511000012
@article{10_1017_S0017089511000012,
author = {ITO, AKIKO},
title = {REMARKS {ON} {THE} {DIVISIBILITY} {OF} {THE} {CLASS} {NUMBERS} {OF} {IMAGINARY} {QUADRATIC} {FIELDS}},
journal = {Glasgow mathematical journal},
pages = {379--389},
year = {2011},
volume = {53},
number = {2},
doi = {10.1017/S0017089511000012},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000012/}
}
TY - JOUR AU - ITO, AKIKO TI - REMARKS ON THE DIVISIBILITY OF THE CLASS NUMBERS OF IMAGINARY QUADRATIC FIELDS JO - Glasgow mathematical journal PY - 2011 SP - 379 EP - 389 VL - 53 IS - 2 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000012/ DO - 10.1017/S0017089511000012 ID - 10_1017_S0017089511000012 ER -
%0 Journal Article %A ITO, AKIKO %T REMARKS ON THE DIVISIBILITY OF THE CLASS NUMBERS OF IMAGINARY QUADRATIC FIELDS %J Glasgow mathematical journal %D 2011 %P 379-389 %V 53 %N 2 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089511000012/ %R 10.1017/S0017089511000012 %F 10_1017_S0017089511000012
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