Higher Siegel--Weil formula for unitary groups II: corank one terms
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911063204691968 |
|---|---|
| author | Feng, Tony Howard, Benjamin Mkrtchyan, Mikayel |
| author_facet | Feng, Tony Howard, Benjamin Mkrtchyan, Mikayel |
| contents | We prove the higher Siegel--Weil formula for \emph{corank one} terms, relating (1) the $r^{\rm th}$ central derivatives of corank one Fourier coefficients of Siegel--Eisenstein series, and (2) the degrees of special cycles of virtual dimension 0 on the moduli stack of Hermitian shtukas with $r$ legs. Notably, the formula holds for all $r$, regardless of the order of vanishing of the Eisenstein series. This extends earlier work of Feng--Yun--Zhang, who proved the higher Siegel--Weil formula for the non-singular (corank zero) terms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13473 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher Siegel--Weil formula for unitary groups II: corank one terms Feng, Tony Howard, Benjamin Mkrtchyan, Mikayel Number Theory Algebraic Geometry Representation Theory We prove the higher Siegel--Weil formula for \emph{corank one} terms, relating (1) the $r^{\rm th}$ central derivatives of corank one Fourier coefficients of Siegel--Eisenstein series, and (2) the degrees of special cycles of virtual dimension 0 on the moduli stack of Hermitian shtukas with $r$ legs. Notably, the formula holds for all $r$, regardless of the order of vanishing of the Eisenstein series. This extends earlier work of Feng--Yun--Zhang, who proved the higher Siegel--Weil formula for the non-singular (corank zero) terms. |
| title | Higher Siegel--Weil formula for unitary groups II: corank one terms |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2507.13473 |