Eligible integers represented by positive ternary quadratic forms
Volume 179 / 2017
Acta Arithmetica 179 (2017), 17-23
MSC: 11E20, 11F37.
DOI: 10.4064/aa8498-2-2017
Published online: 24 May 2017
Abstract
Assume that is a positive definite integral ternary quadratic form. Let N_f denote the level of f. Assume that there are exactly two classes in gen(f) and let g be a representative of the other class. Assume further that f and g are in the same spinor genus. We show that if M with (M,N_f)=1 is an eligible integer which is not square-free, then it can be represented by f. This generalizes Ono and Soundararajan’s 1997 result for f=x_1^2+x_2^2+10x_3^2, Wang and Pei’s 2001 result for f=x_1^2+7x_2^2+7x_3^2 and Kelley’s 2001 result for f=x_1^2+x_2^2+7x_3^2.
