International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 12, Pages 637-646
doi:10.1155/S0161171204203076
On the number of representations of positive
integers by quadratic forms as the basis of the space
S4(Γ0(47),1)
Department of Mathematics, Faculty of Science, University of Uludag, Görükle, Bursa 16059, Turkey
Received 11 March 2002
Copyright © 2004 Ahmet Tekcan and Osman Bızım. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
The number of representations of positive integers by quadratic
forms F1=x12+x1x2+12x22 and
G1=3x12+x1x2+4x22 of discriminant −47 are
given. Moreover, a basis for the space S4(Γ0(47),1)
are constructed, and the formulas for r(n;F4), r(n;G4),
r(n;F3⊕G1), r(n;F2⊕G2), and
r(n;F1⊕G3) are derived.