Preprint: Twisting moduli for gl(2) : WestminsterResearch

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Title	Preprint: Twisting moduli for gl(2)
Authors	Bedert, B., Cooper, G., Oliver, T. and Zhang, P.
Description	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).
Year	2020
Output media	arXiv preprint
Publisher	arXiv
Published	05 Mar 2020
ISSN	2331-8422
Digital Object Identifier (DOI)	https://doi.org/10.48550/arxiv.2003.02557
Journal	ARXIV

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Preprint: Twisting moduli for gl(2)

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