On the Spectral Large Sieve Inequality for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911965978296320 |
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| author | Qi, Zhi |
| author_facet | Qi, Zhi |
| contents | In this paper, we introduce concise expressions for the complex Bessel integral that enables us to improve the spectral large sieve inequality of Watt for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$. Our result is optimistic in the case when the average of spectral parameters is on a square centered at $(0, 0)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Spectral Large Sieve Inequality for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$ Qi, Zhi Number Theory 11F30, 11F72, 33C10 In this paper, we introduce concise expressions for the complex Bessel integral that enables us to improve the spectral large sieve inequality of Watt for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$. Our result is optimistic in the case when the average of spectral parameters is on a square centered at $(0, 0)$. |
| title | On the Spectral Large Sieve Inequality for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$ |
| topic | Number Theory 11F30, 11F72, 33C10 |
| url | https://arxiv.org/abs/2404.09085 |