Fourier Coefficients and Algebraic Cusp Forms on $\mathrm{U}(2,n)$

Abstract

We establish a theory of scalar Fourier coefficients for a class of non-holomorphic, automorphic forms on the quaternionic real Lie group $\mathrm{U}(2,n)$. By studying the theta lifts of holomorphic modular forms from $\mathrm{U}(1,1)$, we apply this theory to obtain examples of non-holomorphic cusp forms on $\mathrm{U}(2,n)$ whose Fourier coefficients are algebraic numbers.

The proof of lemma 5.3 has been corrected so that Theorem 1.3 is valid when $\ell >n+1$. Remarks 3.5 and 5.5 were included for compatibility with existing literature. Exposition has been improved