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<p>We develop a soft method for deriving lower bounds for the Riemann zeta function on <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11139_2025_1202_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\(\operatorname {Re}(s)=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>Re</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> using the theory of <i>GL</i>(3) Eisenstein series.</p>

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Lower bounds for \(\zeta (1+it)\) and GL(3)

  • 期刊论文

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  • 发表日期：

    2025年8月30日

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  • Xiaoqing Li

摘要

We develop a soft method for deriving lower bounds for the Riemann zeta function on \(\operatorname {Re}(s)=1\) Re ( s ) = 1 using the theory of GL(3) Eisenstein series.