Twisting moduli for GL(2)
Number Theory
2023-07-14 v1
Abstract
We prove various converse theorems for automorphic forms on \Gamma_0(N), each assuming fewer twisted functional equations than the last. We show that no twisting at all is needed for holomorphic modular forms in the case that N is 18, 20, or 24 - these integers are the smallest multiples of 4 or 9 not covered by earlier work of Conrey-Farmer. This development is a consequence of finding generating sets for \Gamma_0(N) such that each generator can be written as a product of special matrices. As for real-analytic Maass forms of even (resp. odd) weight we prove the analogous statement for N=1,...12,16,18 (resp. N=1,...,12,14,15,16,17,18,20,23,24).
Keywords
Cite
@article{arxiv.2003.02557,
title = {Twisting moduli for GL(2)},
author = {Benjamin Bedert and George Cooper and Thomas Oliver and Pengcheng Zhang},
journal= {arXiv preprint arXiv:2003.02557},
year = {2023}
}
Comments
17 pages, 2 tables