### Phantom holomorphic projection

Heilbronn Number Theory Seminar

14th November 2018, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

Orthogonal holomorphic projection of non-holomorphic modular forms is an important tool for arithmetic applications. Sturm's convolution method describes the holomorphic projection reliably for Siegel modular forms of large weights. We discuss Sturm's operator for small weights, the critical weight being one larger than the group rank. In this case it does not only produce the terms of holomorphic projection but also so-called phantom terms. We give a spectral theoretic interpretation of these phantom terms.

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