Cusp Forms in 𝑆𝟒(Γ𝟎(𝟒𝟕)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant −𝟒𝟕
A basis of 𝑆4(Γ0(47)) is given and the formulas for the number of representations of positive integers by some direct sum of the quadratic forms 𝑥21+𝑥1𝑥2+12𝑥22, 2𝑥21±𝑥1𝑥2+6𝑥22, 3𝑥21±𝑥1𝑥2+4𝑥22 are determined.
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2012-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2012/303492 |