English

A regularized theta lift on the symmetric space of $SL_N$

Number Theory 2025-12-30 v1

Abstract

We define a regularized lift from harmonic weak Maass forms of weight 2N2-N to differential forms of degree N1N-1 on the symmetric space \SLN(R)/\SO(N)\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.

Keywords

Cite

@article{arxiv.2512.23052,
  title  = {A regularized theta lift on the symmetric space of $SL_N$},
  author = {Romain Branchereau},
  journal= {arXiv preprint arXiv:2512.23052},
  year   = {2025}
}