A Study on the Number of Representations of an Integer into Certain Quadratic Forms
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911761731420160 |
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| author | Kashyap, Kritika |
| author_facet | Kashyap, Kritika |
| contents | Let $a_k(n)$ denotes the number of representations of a non-negative integer $n$ as sum of $k$ quadratic forms of the type $x^2+xy+y^2$ and $a_{λ_1,λ_2,λ_3\dotsλ_k}(n)$ denotes the number of representations $n$ as a linear combination of $k$ quadratic forms of the aforementioned type, where $λ_i$'s are positive integers. The expressions for $a_k(n)$ and $a_{λ_1,λ_2,λ_3\dotsλ_k}(n)$ for different values of $k$ and $λ_i$ are available in the literature. In this project, we attempt to find relationships among some of these particular $a_{λ_1,λ_2,λ_3\dotsλ_k}(n)$'s in a generalized manner. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07811 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Study on the Number of Representations of an Integer into Certain Quadratic Forms Kashyap, Kritika History and Overview Number Theory Let $a_k(n)$ denotes the number of representations of a non-negative integer $n$ as sum of $k$ quadratic forms of the type $x^2+xy+y^2$ and $a_{λ_1,λ_2,λ_3\dotsλ_k}(n)$ denotes the number of representations $n$ as a linear combination of $k$ quadratic forms of the aforementioned type, where $λ_i$'s are positive integers. The expressions for $a_k(n)$ and $a_{λ_1,λ_2,λ_3\dotsλ_k}(n)$ for different values of $k$ and $λ_i$ are available in the literature. In this project, we attempt to find relationships among some of these particular $a_{λ_1,λ_2,λ_3\dotsλ_k}(n)$'s in a generalized manner. |
| title | A Study on the Number of Representations of an Integer into Certain Quadratic Forms |
| topic | History and Overview Number Theory |
| url | https://arxiv.org/abs/2401.07811 |