Scholarlink

<p>Let <i>S</i>(<i>y</i>) be the set of <i>y</i>-friable integers, and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10013_2025_753_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(s_{\varphi }(n)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>s</mi> <mi>φ</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> denotes the Zeckendorf sum-of-digits function of the integer <i>n</i>. In this paper, we aim to prove the equidistribution of the subsequence <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10013_2025_753_Article_IEq2.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="90" /> </InlineMediaObject> <EquationSource Format="TEX">\((s_{\varphi }(n))_{n \in S(y)}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>s</mi> <mi>φ</mi> </msub> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>n</mi> <mo>∈</mo> <mi>S</mi> <mo stretchy="false">(</mo> <mi>y</mi> <mo stretchy="false">)</mo> </mrow> </msub> </math></EquationSource> </InlineEquation> within arithmetic progressions in a specific range of values for <i>y</i>.</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

The Level of Distribution of the Zeckendorf Sum-of-Digits Function over Friable Integers

  • 期刊论文

  • 发表日期：

    2025年9月1日

查看全文
  • Walid Wannes,
  • Hichem Zouari

摘要

Let S(y) be the set of y-friable integers, and \(s_{\varphi }(n)\) s φ ( n ) denotes the Zeckendorf sum-of-digits function of the integer n. In this paper, we aim to prove the equidistribution of the subsequence \((s_{\varphi }(n))_{n \in S(y)}\) ( s φ ( n ) ) n ∈ S ( y ) within arithmetic progressions in a specific range of values for y.