Year: 2026
Type: preprint
Abstract: We formulate a conjectural generalization of the arithmetic Siegel-Weil formula, relating intersection multiplicities of cycles on unitary Rapoport-Zink spaces to central derivatives of local Whittaker functions. The new aspect of the conjecture is that it incorporates the action of certain Hecke correspondences on the Rapoport-Zink space. We verify the conjecture in a low-dimensional case. A significant portion of the paper is devoted to generalizing the classical theory of representation densities for local Hermitian spaces, as this is needed for explicit computation of the relevant Whittaker functions. We expect this generalization to be of independent interest.
Source: arXiv (Cornell University)
Author: Howard, Benjamin
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7213295848