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<p>We study the distribution of the sequence of integers <i>d</i>(<i>n</i><sup>2</sup>) under the assumption of the strong Riemann hypothesis. Under this assumption, we provide a refined asymptotic formula for the sum <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\sum_{n\leqslant x}}d(n^2)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <munder> <mo>∑</mo> <mrow> <mi>n</mi> <mo>⩽</mo> <mi>x</mi> </mrow> </munder> </mrow> <mi>d</mi> <mo stretchy="false">(</mo> <msup> <mi>n</mi> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> with an improved error term by extracting some more main terms.</p>

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On the distribution of the sequence of integers d(n2)

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • Venkatasubbareddy Kampamolla,
  • Sankaranarayanan Ayyadurai

摘要

We study the distribution of the sequence of integers d(n2) under the assumption of the strong Riemann hypothesis. Under this assumption, we provide a refined asymptotic formula for the sum \({\sum_{n\leqslant x}}d(n^2)\) ∑ n ⩽ x d ( n 2 ) with an improved error term by extracting some more main terms.