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<p>In this paper, we prove that there exist Whittaker and Schwartz functions such that the local Flicker integrals are non-vanishing for all complex values of <i>s</i>, and the local Bump–Friedberg integrals are non-vanishing for all complex pairs <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1096_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="50" /> </InlineMediaObject> <EquationSource Format="TEX">\((s_1,s_2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>s</mi> <mn>2</mn> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. As a corollary, we determine the potential locations of poles for their corresponding partial L-functions.</p>

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Non-vanishing of certain integral representations

  • 期刊论文

  • 发表日期：

    2025年5月24日

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  • Akash Yadav

摘要

In this paper, we prove that there exist Whittaker and Schwartz functions such that the local Flicker integrals are non-vanishing for all complex values of s, and the local Bump–Friedberg integrals are non-vanishing for all complex pairs \((s_1,s_2)\) ( s 1 , s 2 ) . As a corollary, we determine the potential locations of poles for their corresponding partial L-functions.