On Borcherds Products Associated with Lattices of Prime Discriminant
By Jan H. Bruinier, Michael Bundschuh. 2003
71 citations recorded by the source corpus.
We show that certain spaces of vector valued modular forms are isomorphic to spaces of scalar valued modular forms whose Fourier coefficients are supported on suitable progressions.As an application we give a very explicit description of Borcherds products on Hilbert modular surfaces.
View Paper: https://www.semanticscholar.org/paper/92a4c497f149aa19444dd2ad531edb927b080f11
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- Jose Ignacio Burgos Gil
- Tonghai Yang
- Jan H. Bruinier
- U. Kuehn
- Ken Ichi Ono
- Kathrin Bringmann
- S. Kudla
- William Duke
Citations in the corpus
- CM-values of Hilbert modular functions (2006, methodology): “k ( p ,� p) ,t hen DN(g) is in Sk(Γ) by [Za] §5. For general g it follows by [Bo1] Theorem 14.3 (combined with Theorem 5 of [ BB ]) that DN(g) ∈ Mk(Γ).”
- Borcherds products and arithmetic intersection theory on Hilbert modular surfaces (2003, methodology): “χD)) for the subspace of holomorphic modular forms (respectively cusp forms). For ǫ∈ {±1} we let Aǫ k (D,χD) be the subspace of all f= P n∈Z c(n)q n in A k(D,χD), for which c(n) = 0 if χD(n) = −ǫ(cf. [BB]). A classical Lemma due to Hecke implies that Ak(D,χD) = A + k (D,χD)⊕ A − k (D,χD). (4.1) Fina”