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arXiv · 2404.09085

On the Spectral Large Sieve Inequality for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$

Zhi Qi
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Abstract

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 $(0, 0)$.

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Zhi Qi. 2024-04-13. On the Spectral Large Sieve Inequality for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$. https://arxiv.org/abs/2404.09085

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