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<p>Let <i>F</i> be a non-archimedean local field of characteristic zero. In this paper we construct examples of supercuspidal representations showing that the bound <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\([\frac{N}{2}]\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">[</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> <mo stretchy="false">]</mo> </mrow> </math></EquationSource> </InlineEquation> for the local converse theorem of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\operatorname {GL}}_N(F)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mo>GL</mo> <mi>N</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>F</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> is sharp, <i>N</i> general, when the residual characteristic of <i>F</i> is bigger than <i>N</i>.</p>

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On the sharpness of the bound for the local converse theorem of p-adic \(\operatorname {GL}_N\), general N

  • 期刊论文

  • 发表日期：

    2026年6月1日

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  • Moshe Adrian

摘要

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