Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.06368 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909071059189760 |
|---|---|
| author | Zhu, Baiqing |
| author_facet | Zhu, Baiqing |
| contents | For arbitrary level $N$, we relate the generating series of codimension 2 special cycles on $\mathcal{X}_{0}(N)$ to the derivatives of a genus 2 Eisenstein series, especially the singular terms of both sides. On the analytic side, we use difference formulas of local densities to relate the singular Fourier coefficients of the genus 2 Eisenstein series to the nonsingular Fourier coefficients of a genus 1 Eisenstein series. On the geometric side, we study the reduction of cusps to compute the divisor class of the Hodge bundle and the heights of special divisors. When $N$ is square-free, this gives a different proof of the main results in the works of Du, Yang and Sankaran, Shi, and Yang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06368 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic Siegel-Weil formula on $\mathcal{X}_0(N)$: singular terms Zhu, Baiqing Number Theory For arbitrary level $N$, we relate the generating series of codimension 2 special cycles on $\mathcal{X}_{0}(N)$ to the derivatives of a genus 2 Eisenstein series, especially the singular terms of both sides. On the analytic side, we use difference formulas of local densities to relate the singular Fourier coefficients of the genus 2 Eisenstein series to the nonsingular Fourier coefficients of a genus 1 Eisenstein series. On the geometric side, we study the reduction of cusps to compute the divisor class of the Hodge bundle and the heights of special divisors. When $N$ is square-free, this gives a different proof of the main results in the works of Du, Yang and Sankaran, Shi, and Yang. |
| title | Arithmetic Siegel-Weil formula on $\mathcal{X}_0(N)$: singular terms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.06368 |