Scholarlink

<p>We prove and generalize some recent conjectures of Z.-W. Sun on infinite series whose summands involve products of harmonic numbers and several binomial coefficients. We evaluate various classes of infinite sums in closed form by interpreting them as automorphic objects on the moduli spaces for Legendre curves <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(Y^{ g+1}=(1-X)^{ g}X(1-t X)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>Y</mi> <mrow> <mi>g</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>-</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> <mi>g</mi> </msup> <mi>X</mi> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo>-</mo> <mi>t</mi> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of positive genera <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\( g\in \{1,2,3,5\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>∈</mo> <mo stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>5</mn> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>.</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

Notes on certain binomial harmonic sums of Sun’s type

  • 期刊论文

  • 发表日期：

    2026年3月7日

查看全文
  • Yajun Zhou

摘要

We prove and generalize some recent conjectures of Z.-W. Sun on infinite series whose summands involve products of harmonic numbers and several binomial coefficients. We evaluate various classes of infinite sums in closed form by interpreting them as automorphic objects on the moduli spaces for Legendre curves \(Y^{ g+1}=(1-X)^{ g}X(1-t X)\) Y g + 1 = ( 1 - X ) g X ( 1 - t X ) of positive genera \( g\in \{1,2,3,5\}\) g ∈ { 1 , 2 , 3 , 5 } .