#### Vol. 316, No. 1, 2022

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Nearly holomorphic automorphic forms on $\mathrm{Sp}_{2n}$ with sufficiently regular infinitesimal characters and applications

### Shuji Horinaga

Vol. 316 (2022), No. 1, 81–129
##### Abstract

We decompose the space of nearly holomorphic Hilbert–Siegel automorphic forms as representations of the adele group under certain assumptions. We also give an application for classical holomorphic Hilbert–Siegel modular forms. In particular, we show the surjectivity of the global Siegel operator $\stackrel{~}{\Phi }$ for certain congruence subgroups with large weights.

##### Keywords
Siegel modular forms, Eisenstein series, nearly holomorphic modular forms
##### Mathematical Subject Classification
Primary: 11F30, 11F41, 11M36
Secondary: 11F22