International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 9-12, 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)
Ahmet Tekcan
and Osman Bizim
Department of Mathematics, Faculty of Science, University of Uludag, Görükle, Bursa 16059, Turkey
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.