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<p>We prove that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(|t\zeta(1+it)| &gt; 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">|</mo> <mi>t</mi> <mi>ζ</mi> <mo stretchy="false">(</mo> <mn>1</mn> <mo>+</mo> <mi>i</mi> <mi>t</mi> <mo stretchy="false">)</mo> <mo stretchy="false">|</mo> <mo>&gt;</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(t\in \mathbb{R}\setminus \{0\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>∈</mo> <mi mathvariant="double-struck">R</mi> <mo lspace="0.15em" rspace="0.15em" stretchy="false">\</mo> <mo stretchy="false">{</mo> <mn>0</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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An inequality satisfied by the Riemann zeta-function on the \(1\)-line

  • 期刊论文

  • 发表日期：

    2026年6月19日

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  • C. Y. Yıldırım

摘要

We prove that \(|t\zeta(1+it)| > 1\) | t ζ ( 1 + i t ) | > 1 for \(t\in \mathbb{R}\setminus \{0\}\) t ∈ R \ { 0 } .