Affiliation:
1. Département de mathématiques et applications , École Normale Supérieure , Paris , France
Abstract
Abstract
We consider the Kudla–Millson theta series associated to a quadratic space of signature
(
N
,
N
)
{(N,N)}
. By combining a “see-saw” argument with the Siegel–Weil formula, we show that its (regularized) integral along a torus attached to a totally real field of degree N is the diagonal restriction of an Eisenstein series. It allows us to express the Fourier coefficients of the diagonal restriction as intersection numbers, which generalizes a result of Darmon, Pozzi and Vonk to totally real fields.
Funder
Horizon 2020 Framework Programme
Subject
Applied Mathematics,General Mathematics
Reference22 articles.
1. R. Bott and L. W. Tu,
Differential Forms in Algebraic Topology,
Grad. Texts in Math. 82,
Springer, New York, 1982.
2. R. Branchereau,
Diagonal restriction and denominators of some Eisenstein cohomology classes,
PhD thesis, PSL Université, Paris, 2022.
3. R. Branchereau,
The Kudla–Millson form via the Mathai–Quillen formalism, submitted.
4. D. Bump,
Automorphic Forms and Representations,
Cambridge Stud. Adv. Math. 55,
Cambridge University, Cambridge, 1997.
5. H. Darmon, A. Pozzi and J. Vonk,
Diagonal restrictions of p-adic Eisenstein families,
Math. Ann. 379 (2021), no. 1–2, 503–548.