Scholarlink

<p>Partial fraction expansions related to Riemann’s xi function and the Dirichlet series <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\frac{1}{1^s}-\frac{1}{3^s}+\frac{1}{5^s}-\frac{1}{7^s}+\cdots \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfrac> <mn>1</mn> <msup> <mn>1</mn> <mi>s</mi> </msup> </mfrac> <mo>-</mo> <mfrac> <mn>1</mn> <msup> <mn>3</mn> <mi>s</mi> </msup> </mfrac> <mo>+</mo> <mfrac> <mn>1</mn> <msup> <mn>5</mn> <mi>s</mi> </msup> </mfrac> <mo>-</mo> <mfrac> <mn>1</mn> <msup> <mn>7</mn> <mi>s</mi> </msup> </mfrac> <mo>+</mo> <mo>⋯</mo> </mrow> </math></EquationSource> </InlineEquation> are given. Also a sufficient condition for the Riemann Hypothesis (<b>RH</b>) to hold is shown. This is related to results given in [<CitationRef CitationID="CR6">6</CitationRef>] or [<CitationRef CitationID="CR9">9</CitationRef>].</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A partial fraction expansion related to Riemann’s xi function

  • 期刊论文

  • 发表日期：

    2025年8月31日

查看全文
  • Panzone Pablo Andres

摘要

Partial fraction expansions related to Riemann’s xi function and the Dirichlet series \(\frac{1}{1^s}-\frac{1}{3^s}+\frac{1}{5^s}-\frac{1}{7^s}+\cdots \) 1 1 s - 1 3 s + 1 5 s - 1 7 s + ⋯ are given. Also a sufficient condition for the Riemann Hypothesis (RH) to hold is shown. This is related to results given in [6] or [9].