The Ramanujan-Petersson and Selberg conjectures for Maass forms
Group Theory
2026-02-13 v16 Number Theory
Abstract
We prove the Ramanujan-Petersson conjecture for Maass forms of the group , with the help of automorphic distribution theory and pseudodifferential analysis. The first notion is an alternative to classical automorphic function theory, in which the plane takes the place usually ascribed to the hyperbolic half-plane. The Selberg conjecture for Hecke's group follows as well.
Cite
@article{arxiv.2001.10956,
title = {The Ramanujan-Petersson and Selberg conjectures for Maass forms},
author = {Andr'e Unterberger},
journal= {arXiv preprint arXiv:2001.10956},
year = {2026}
}
Comments
The (pseudodifferential) Section 7 has been rewritten, so as to make easier reading