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International Journal of Mathematics and Mathematical Sciences
Volume 2012, Article ID 303492, 10 pages
http://dx.doi.org/10.1155/2012/303492
Letter to the Editor

Cusp Forms in 𝑆 𝟒 ( Γ 𝟎 ( 𝟒 𝟕 ) ) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant 𝟒 𝟕

Department of Mathematics, Faculty of Arts and Sciences, Fatih University, Buyukcekmece, 34500 Istanbul, Turkey

Received 20 August 2011; Accepted 15 September 2011

Copyright © 2012 Barış Kendirli. 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

A basis of 𝑆 4 ( Γ 0 ( 4 7 ) ) is given and the formulas for the number of representations of positive integers by some direct sum of the quadratic forms 𝑥 2 1 + 𝑥 1 𝑥 2 + 1 2 𝑥 2 2 , 2 𝑥 2 1 ± 𝑥 1 𝑥 2 + 6 𝑥 2 2 , 3 𝑥 2 1 ± 𝑥 1 𝑥 2 + 4 𝑥 2 2 are determined.