Discriminantal divisors and binary quadratic forms
Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 69-73
Voir la notice de l'article provenant de la source Cambridge University Press
An ancipital form is a form [a, b, c] in which b= 0 or b= a; these fall into pairs of associates: [a, 0, c] and [c, 0, a] (type 1), and [a, a, c] and [4c–a, 4c–a, c] (type 2). The set of discriminantal divisors of discriminant d is formed by choosing, from each pair of primitive associate ancipital forms of discriminant d, exactly one of the two leading coefficients. In this article we study representations of discriminantal divisors of a given discriminant by binary quadratic forms of that discriminant, previously studied by the author and by G. Pall. We are concerned here with discriminants d= 4kpq, where k ≥ 1, p = 1, q = 3 (mod 4) are primes, and d = 4kp, where k ≥ 1 and p is an odd prime. This investigation arose in connection with the search for integral solutions of x2 –Dy2 = – 1.
Brown, Ezra. Discriminantal divisors and binary quadratic forms. Glasgow mathematical journal, Tome 13 (1972) no. 1, pp. 69-73. doi: 10.1017/S0017089500001397
@article{10_1017_S0017089500001397,
author = {Brown, Ezra},
title = {Discriminantal divisors and binary quadratic forms},
journal = {Glasgow mathematical journal},
pages = {69--73},
year = {1972},
volume = {13},
number = {1},
doi = {10.1017/S0017089500001397},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500001397/}
}
[1] 1.Brown, Ezra, Representations of discriminantal divisors by binary quadratic forms, J. Number Theory 3 (1971), 213–225. Google Scholar | DOI
[2] 2.Pall, Gordon, On generalized quaternions, Trans. Amer. Math. Soc. 59 (1946), 280–332. Google Scholar
[3] 3.Pall, Gordon, Discriminantal divisors of binary quadratic forms, J. Number Theory 1 (1969), 525–532. Google Scholar | DOI
Cité par Sources :