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A GL(3) converse theorem via a "beyond endoscopy" approach

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arxiv 2401.04037 v2 pith:QOJ64EG4 submitted 2024-01-08 math.NT

Valentin Blomer , Wing Hong Leung This is my paper · ORCID
classification math.NT
keywords beyondconverseendoscopytheoremapproachfirstformsgive
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abstract

We give a new proof of the converse theorem for Maass forms on ${\rm GL}(3)$ using a technique that is inspired by Langlands' philosophy of "beyond endoscopy", thereby implementing these ideas for the first time in a higher rank setting.

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  1. Hybrid bounds for ${\rm{GL}}(4)\times {\rm{GL}}(1)$ twisted $L$-functions

    math.NT 2025-01 reject novelty 6.0 of 10

    A hybrid subconvex bound for L(1/2, Pi tensor chi) is claimed for prime level P and conductor M with M^{1/5} < P < M^{2/5}, but the final exponent passage in the proof is not justified.

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