On Eisenstein series on quaternion unitary groups of degree 2. (English) Zbl 0966.11023

Hirai, Yoshikazu

J. Math. Soc. Japan 51, No. 1, 93-128 (1999).

The author considers Eisenstein series on certain quaternion unitary groups. Using Shimura’s method the Fourier expansion can be calculated explicitly. This leads to a direct result on the analytic continuation and functional equation without the use of Langlands’ theory. Moreover special values and the explicit formulas yield holomorphic Eisenstein series and Oda’s lifted cusp forms. Several tables with numerical examples are included.

Reviewer: A.Krieg (Aachen)

MSC:

11F55	Other groups and their modular and automorphic forms (several variables)
11F30	Fourier coefficients of automorphic forms

Keywords:

automorphic forms; Eisenstein series; quaternion unitary groups; Fourier expansion; analytic continuation; functional equation; special values