On the Spectral Large Sieve Inequality for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$
Number Theory
2024-07-26 v3
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 . Our result is optimistic in the case when the average of spectral parameters is on a square centered at .
Cite
@article{arxiv.2404.09085,
title = {On the Spectral Large Sieve Inequality for $\mathrm{PGL}_2 (\mathbb{Z}[i]) \backslash \mathrm{PGL}_2 (\mathbb{C})$},
author = {Zhi Qi},
journal= {arXiv preprint arXiv:2404.09085},
year = {2024}
}
Comments
12 pages; Theorem 3 (self) improved; some typos corrected