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Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2022

Diagonal restriction of Eisenstein series and Kudla-Millson theta lift

Résumé

We consider the Kudla-Millson theta series associated to a quadratic space of signature $(N,N)$. 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-Vonk to totally real fields.

Dates et versions

hal-04001203 , version 1 (22-02-2023)

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Citer

Romain Branchereau. Diagonal restriction of Eisenstein series and Kudla-Millson theta lift. 2023. ⟨hal-04001203⟩

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