Nearly holomorphic automorphic forms on Sp(2n) with sufficiently regular infinitesimal characters and applications

TL;DR

This paper decomposes nearly holomorphic automorphic forms on Sp(2n) into representations and applies the results to classical Hilbert-Siegel modular forms, proving the surjectivity of the global Siegel operator under specific conditions.

Contribution

It provides a new decomposition of nearly holomorphic automorphic forms on Sp(2n) and demonstrates the surjectivity of the global Siegel operator for certain congruence subgroups.

Findings

Decomposition of nearly holomorphic Hilbert-Siegel automorphic forms.

Application to classical holomorphic Hilbert-Siegel modular forms.

Surjectivity of the global Siegel operator for large weights.

Abstract

In this paper, 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 for certain congruence subgroups with large weights.