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 Φ~ 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
Milestones
Received: 17 November 2020
Revised: 19 July 2021
Accepted: 23 October 2021
Published: 26 February 2022
Authors
Shuji Horinaga
Center for Data Science
Tokyo University of Science
Tokyo
Japan