English

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 U(2,n)\mathrm{U}(2,n). By studying the theta lifts of holomorphic modular forms from U(1,1)\mathrm{U}(1,1), we apply this theory to obtain examples of non-holomorphic cusp forms on U(2,n)\mathrm{U}(2,n) whose Fourier coefficients are algebraic numbers.

Keywords

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

R2 v1 2026-06-28T16:08:16.064Z