Fourier Coefficients and Algebraic Cusp Forms on $\mathrm{U}(2,n)$
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| Format: | Preprint |
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2024
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| _version_ | 1866909803030249472 |
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| author | Hilado, Anton McGlade, Finn Yan, Pan |
| author_facet | Hilado, Anton McGlade, Finn Yan, Pan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17743 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fourier Coefficients and Algebraic Cusp Forms on $\mathrm{U}(2,n)$ Hilado, Anton McGlade, Finn Yan, Pan Number Theory Representation Theory 11F30 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. |
| title | Fourier Coefficients and Algebraic Cusp Forms on $\mathrm{U}(2,n)$ |
| topic | Number Theory Representation Theory 11F30 |
| url | https://arxiv.org/abs/2404.17743 |