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

Shuji Horinaga

Vol. 316 (2022), No. 1, 81–129

DOI: 10.2140/pjm.2022.316.81

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 $\tilde{\Phi }$ 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

Milestones

Received: 17 November 2020

Revised: 19 July 2021

Accepted: 23 October 2021

Published: 26 February 2022