A regularized theta lift on the symmetric space of $SL_N$
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914223238414336 |
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| author | Branchereau, Romain |
| author_facet | Branchereau, Romain |
| contents | We define a regularized lift from harmonic weak Maass forms of weight $2-N$ to differential forms of degree $N-1$ on the symmetric space $\SL_N(\R)/\SO(N)$, that are smooth outside of certain modular symbols. We show that this lift is adjoint to the derivative of a theta lift. We compute periods of the regularized lift over tori and relate them to Fourier coefficients of Hilbert-Eisenstein series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23052 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A regularized theta lift on the symmetric space of $SL_N$ Branchereau, Romain Number Theory We define a regularized lift from harmonic weak Maass forms of weight $2-N$ to differential forms of degree $N-1$ on the symmetric space $\SL_N(\R)/\SO(N)$, that are smooth outside of certain modular symbols. We show that this lift is adjoint to the derivative of a theta lift. We compute periods of the regularized lift over tori and relate them to Fourier coefficients of Hilbert-Eisenstein series. |
| title | A regularized theta lift on the symmetric space of $SL_N$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.23052 |