Higher Siegel--Weil formula for unitary groups II: corank one terms

2025/07/17 by Tony Feng, Benjamin Howard, Feng, Tony +3
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2507.13473

openalex publication_date 2025/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the higher Siegel--Weil formula for 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.

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