Twisting moduli for GL(2) : WestminsterResearch

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Title	Twisting moduli for GL(2)
Type	Journal article
Authors	Bedert, B., Cooper, G., Oliver, T. and Zhang, P.
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\in{18,20,24} - 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 1\leq N\leq 12, 14\leq N\leq18 and N\in{16,18} (resp. 1\leq N\leq 12, 14\leq N\leq 18 and N\in{20,23,24}).
Journal	Journal of Number Theory
Journal citation	217, pp. 142-162
ISSN	0022-314X
	1096-1658
Year	2020
Publisher	Elsevier
Accepted author manuscript	Accepted-twisting-moduli.pdf License CC BY-NC-ND 4.0 File Access Level Open (open metadata and files)
Digital Object Identifier (DOI)	https://doi.org/10.1016/j.jnt.2020.04.008
Web address (URL)	https://www.sciencedirect.com/science/article/abs/pii/S0022314X20301219#!
Published in print	Dec 2020
Published online	19 May 2020

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Twisting moduli for GL(2)

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