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Higher pullbacks of modular forms on orthogonal groups

Authors
  • Williams, Brandon1
  • 1 RWTH Aachen University, 52056 , (Germany)
Type
Published Article
Journal
Forum Mathematicum
Publisher
De Gruyter
Publication Date
Mar 20, 2021
Volume
33
Issue
3
Pages
631–652
Identifiers
DOI: 10.1515/forum-2020-0066
Source
De Gruyter
Keywords
License
Yellow

Abstract

We apply differential operators to modular forms on orthogonal groups O⁢(2,ℓ){\mathrm{O}(2,\ell)} to construct infinite families of modular forms on special cycles. These operators generalize the quasi-pullback. The subspaces of theta lifts are preserved; in particular, the higher pullbacks of the lift of a (lattice-index) Jacobi form ϕ are theta lifts of partial development coefficients of ϕ. For certain lattices of signature (2,2){(2,2)} and (2,3){(2,3)}, for which there are interpretations as Hilbert–Siegel modular forms, we observe that the higher pullbacks coincide with differential operators introduced by Cohen and Ibukiyama.

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