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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.11621 |
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| _version_ | 1866915856799236096 |
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| author | Soni, Ekta Datt, M. S. Sankaranarayanan, A. |
| author_facet | Soni, Ekta Datt, M. S. Sankaranarayanan, A. |
| contents | Let $\mathbb{K}$ be a non-normal algebraic number field of cubic degree given by the polynomial $x^{3}+ax^{2}+bx+c$ of discriminant $D_{\mathbb{K}}<0$. For sufficiently large $x$, we establish an asymptotic formula for the hybrid sum $$\sum\limits_{\substack{n= \sum_{i=1}^{8}n_{i}^{2}\leq x\\ (n_{1},n_{2},n_{3},n_{4},n_{5},n_{6},n_{7},n_{8})\in \mathbb{Z}^{8} }} a_{\mathbb{K}}^{2}(n)$$ with a tight error term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11621 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the discrete mean square of certain hybrid sum involving $a_{\mathbb{K}}(n)$ Soni, Ekta Datt, M. S. Sankaranarayanan, A. Number Theory Let $\mathbb{K}$ be a non-normal algebraic number field of cubic degree given by the polynomial $x^{3}+ax^{2}+bx+c$ of discriminant $D_{\mathbb{K}}<0$. For sufficiently large $x$, we establish an asymptotic formula for the hybrid sum $$\sum\limits_{\substack{n= \sum_{i=1}^{8}n_{i}^{2}\leq x\\ (n_{1},n_{2},n_{3},n_{4},n_{5},n_{6},n_{7},n_{8})\in \mathbb{Z}^{8} }} a_{\mathbb{K}}^{2}(n)$$ with a tight error term. |
| title | On the discrete mean square of certain hybrid sum involving $a_{\mathbb{K}}(n)$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.11621 |