Eisenstein series part of the primitive representations for even rank quadratic forms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866915034330824704 |
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| author | Kane, Ben Xue, Luhao |
| author_facet | Kane, Ben Xue, Luhao |
| contents | In this paper, we first investigate the relationship between the number of primitive representations of $n$ by quadratic forms and the number of non-primitive ones. We hence obtain a theorem to deal with the Eisenstein series part with quadratic Dirichlet character when deriving the formula for the number of primitive representations of an integer $n$ by even rank quadratic forms from the number of non primitive ones. Formulas for special cases are given as examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_18071 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Eisenstein series part of the primitive representations for even rank quadratic forms Kane, Ben Xue, Luhao Number Theory 11F11, 11F27, 11E20 In this paper, we first investigate the relationship between the number of primitive representations of $n$ by quadratic forms and the number of non-primitive ones. We hence obtain a theorem to deal with the Eisenstein series part with quadratic Dirichlet character when deriving the formula for the number of primitive representations of an integer $n$ by even rank quadratic forms from the number of non primitive ones. Formulas for special cases are given as examples. |
| title | Eisenstein series part of the primitive representations for even rank quadratic forms |
| topic | Number Theory 11F11, 11F27, 11E20 |
| url | https://arxiv.org/abs/2303.18071 |