Diagonal restriction of Eisenstein series and Kudla–Millson theta lift.

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 and Vonk to totally real fields. [ABSTRACT FROM AUTHOR]