On the number of representations of positive integers by quadratic forms as the basis of the space S4(Γ0(47),1)
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....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204203076 |
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| _version_ | 1832561482693345280 |
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| author | Ahmet Tekcan Osman Bızım |
| author_facet | Ahmet Tekcan Osman Bızım |
| author_sort | Ahmet Tekcan |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-287490d6142648bbb74c191a3f77c416 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-287490d6142648bbb74c191a3f77c4162025-02-03T01:24:55ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-0120041263764610.1155/S0161171204203076On the number of representations of positive integers by quadratic forms as the basis of the space S4(Γ0(47),1)Ahmet Tekcan0Osman Bızım1Department of Mathematics, Faculty of Science, University of Uludag, Görükle, Bursa 16059, TurkeyDepartment of Mathematics, Faculty of Science, University of Uludag, Görükle, Bursa 16059, TurkeyThe 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.http://dx.doi.org/10.1155/S0161171204203076 |
| spellingShingle | Ahmet Tekcan Osman Bızım On the number of representations of positive integers by quadratic forms as the basis of the space S4(Γ0(47),1) International Journal of Mathematics and Mathematical Sciences |
| title | On the number of representations of positive
integers by quadratic forms as the basis of the space
S4(Γ0(47),1) |
| title_full | On the number of representations of positive
integers by quadratic forms as the basis of the space
S4(Γ0(47),1) |
| title_fullStr | On the number of representations of positive
integers by quadratic forms as the basis of the space
S4(Γ0(47),1) |
| title_full_unstemmed | On the number of representations of positive
integers by quadratic forms as the basis of the space
S4(Γ0(47),1) |
| title_short | On the number of representations of positive
integers by quadratic forms as the basis of the space
S4(Γ0(47),1) |
| title_sort | on the number of representations of positive integers by quadratic forms as the basis of the space s4 γ0 47 1 |
| url | http://dx.doi.org/10.1155/S0161171204203076 |
| work_keys_str_mv | AT ahmettekcan onthenumberofrepresentationsofpositiveintegersbyquadraticformsasthebasisofthespaces4g0471 AT osmanbızım onthenumberofrepresentationsofpositiveintegersbyquadraticformsasthebasisofthespaces4g0471 |