Fourier Coefficients and Algebraic Cusp Forms on $\mathrm{U}(2,n)$
Number Theory
2025-09-25 v2 Representation Theory
Abstract
We establish a theory of scalar Fourier coefficients for a class of non-holomorphic, automorphic forms on the quaternionic real Lie group . By studying the theta lifts of holomorphic modular forms from , we apply this theory to obtain examples of non-holomorphic cusp forms on whose Fourier coefficients are algebraic numbers.
Cite
@article{arxiv.2404.17743,
title = {Fourier Coefficients and Algebraic Cusp Forms on $\mathrm{U}(2,n)$},
author = {Anton Hilado and Finn McGlade and Pan Yan},
journal= {arXiv preprint arXiv:2404.17743},
year = {2025}
}
Comments
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