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Licensed Unlicensed Requires Authentication Published by De Gruyter March 20, 2021

Higher pullbacks of modular forms on orthogonal groups

  • Brandon Williams EMAIL logo
From the journal Forum Mathematicum

Abstract

We apply differential operators to modular forms on orthogonal groups O(2,) 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) and (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.

MSC 2010: 11F27; 11F55; 11F60

Communicated by Jan Bruinier


Funding statement: This research is supported by a postdoctoral fellowship of the LOEWE research unit Uniformized Structures in Arithmetic and Geometry.

Acknowledgements

I thank Martin Raum for helpful comments, in particular his suggestion to consider Example 6.5.

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Received: 2020-03-11
Revised: 2021-02-09
Published Online: 2021-03-20
Published in Print: 2021-05-01

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