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arXiv · 2211.11698

Diagonal restriction of Eisenstein series and Kudla-Millson theta lift

Romain Branchereau
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Abstract

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.

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Romain Branchereau. 2022-11-21. Diagonal restriction of Eisenstein series and Kudla-Millson theta lift. https://arxiv.org/abs/2211.11698

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