Year: 2025
Type: article
Abstract: ABSTRACT We prove two results on converse theorems for Hilbert modular forms over totally real fields of degree $r>1$. The first result recovers a Hilbert modular form (of some level) from an L-series satisfying functional equations twisted by all the unramified Hecke characters. The second result assumes both the ‘unramified’ functional equations and an Euler product, and recovers a Hilbert modular form of the expected level predicted by the shape of the functional equations. Our result generalizes the current converse theorems for $\mathrm{GL}_2$ in the case of Hilbert modular forms in that we completely remove the assumptions on ramified twists.
Author: Pengcheng Zhang
Institution: Max Planck Institute for Mathematics
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,241
OpenAlex ID: W4415830521