## Journal of the Mathematical Society of Japan

- J. Math. Soc. Japan
- Volume 55, Number 4 (2003), 995-1031.

### A certain Galois action on nearly holomorphic modular forms with respect to a unitary group in three variables

#### Abstract

In this paper we will consider Fourier-Jacobi expansions of nearly holomorphic modular forms on $SU(2,1)$, whose coefficients are nearly holomorphic theta functions, and will construct a certain Galois action on them.

#### Article information

**Source**

J. Math. Soc. Japan, Volume 55, Number 4 (2003), 995-1031.

**Dates**

First available in Project Euclid: 3 October 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.jmsj/1191418761

**Digital Object Identifier**

doi:10.2969/jmsj/1191418761

**Mathematical Reviews number (MathSciNet)**

MR2003757

**Zentralblatt MATH identifier**

1161.11338

**Subjects**

Primary: 11F37: Forms of half-integer weight; nonholomorphic modular forms

Secondary: 11F30: Fourier coefficients of automorphic forms

**Keywords**

Unitary group nearly holomorphic modular form Fourier-Jacobi expansion Galois action

#### Citation

YAMAUCHI, Atsuo. A certain Galois action on nearly holomorphic modular forms with respect to a unitary group in three variables. J. Math. Soc. Japan 55 (2003), no. 4, 995--1031. doi:10.2969/jmsj/1191418761. https://projecteuclid.org/euclid.jmsj/1191418761