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On the sharpness of the bound for the local converse theorem of p-adic GL_N, general N

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arxiv 2303.08656 v2 pith:QXROL3VC submitted 2023-03-15 math.RT math.NT

Moshe Adrian This is my paper
classification math.RTmath.NT
keywords localboundcharacteristicconversegeneraltheorembiggerconstruct
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abstract

Let F be a non-archimedean local field of characteristic zero. In this paper we construct examples of supercuspidal representations showing that the bound $[N/2]$ for the local converse theorem of $GL_N(F)$ is sharp, N general, when the residual characteristic of $F$ is bigger than $N$.

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On the Local Converse Theorem for Depth $\frac{1}{N}$ Supercuspidal Representations of $\text{GL}(2N, F)$

    math.RT 2025-05 conditional novelty 8.0 of 10

    Middle supercuspidals of GL(2N,F) are characterized by twisted gamma factors against tamely ramified quasi-characters and simple supercuspidals of GL(N,F).

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