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Abstract <p>We obtain an asymptotic formula for the sum       <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11472_2025_9871_Article_IEq1.gif" Format="GIF" Height="49" Rendition="HTML" Resolution="72" Type="Linedraw" Width="246" /> </InlineMediaObject> <EquationSource Format="TEX">\(Q(x) = \sum\limits_{\substack{ n \leqslant x \\ r(n + 1) \ne 0 } } \frac{{r(n)}}{{r(n + 1)}}\;\;(x \to + \infty ),\)</EquationSource> <!--DANMath2460158Iudelevich-m1--> </InlineEquation> where <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11472_2025_9871_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="32" /> </InlineMediaObject> <EquationSource Format="TEX">\(r(n)\)</EquationSource> <!--DANMath2460158Iudelevich-m2--> </InlineEquation> denotes the number of representations of <i>n</i> as a sum of two squares.</p>

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On Some Number Theoretic Sum

  • 期刊论文

  • 发表日期：

    2025年2月1日

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  • V. V. Iudelevich

摘要

Abstract

We obtain an asymptotic formula for the sum        \(Q(x) = \sum\limits_{\substack{ n \leqslant x \\ r(n + 1) \ne 0 } } \frac{{r(n)}}{{r(n + 1)}}\;\;(x \to + \infty ),\) where \(r(n)\) denotes the number of representations of n as a sum of two squares.