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Twisting moduli for GL(2)
- Source :
- J. Number Theory 217 (2020) 142-162
- Publication Year :
- 2020
-
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).<br />Comment: 17 pages, 2 tables
- Subjects :
- Mathematics - Number Theory
11F66, 11M41, 11F12
Subjects
Details
- Database :
- arXiv
- Journal :
- J. Number Theory 217 (2020) 142-162
- Publication Type :
- Report
- Accession number :
- edsarx.2003.02557
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1016/j.jnt.2020.04.008