Unfolding and injectivity of the Kudla-Millson lift of genus 1

Abstract

We unfold the theta integrals defining the Kudla-Millson lift of genus 1 associated to even lattices of signature (b,2), where b>2. This enables us to compute the Fourier expansion of such defining integrals and prove the injectivity of the Kudla-Millson lift. Although the latter result has been already proved by Bruinier, our new procedure has the advantage of paving the ground for a strategy to prove the injectivity of the lift also for the cases of general signature and of genus greater than 1.

Article shortened, few typos corrected, main results unchanged. To appear in Math. Z

References in corpus (2)

• Cones of special cycles of codimension 2 on orthogonal Shimura varieties
• Unfolding and injectivity of the Kudla-Millson lift of genus 1

Cited by in corpus (2)

• Unfolding and injectivity of the Kudla-Millson lift of genus 1
• Kudla-Millson lift of toric cycles and restriction of Hilbert modular forms