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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S_{\kappa }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>κ</mi> </msub> </math></EquationSource> </InlineEquation> be the space of cusp forms of weight <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\kappa \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>κ</mi> </math></EquationSource> </InlineEquation> and level one, and let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(S_{\kappa }^{*}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mi>S</mi> <mrow> <mi>κ</mi> </mrow> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation> denote its dual space. In this paper, we find explicit spanning subsets of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(S_{\kappa }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>κ</mi> </msub> </math></EquationSource> </InlineEquation> consisting of Rankin-Cohen brackets of Eisenstein series and explicit subsets of periods that span <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(S_{\kappa }^{*}\)</EquationSource> <EquationSource Format="MATHML"><math> <mmultiscripts> <mi>S</mi> <mrow> <mi>κ</mi> </mrow> <mrow> <mrow /> <mo>∗</mo> </mrow> </mmultiscripts> </math></EquationSource> </InlineEquation>.</p>

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Explicit generators of the space of modular forms

  • 期刊论文

  • 发表日期：

    2026年6月25日

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  • Tianyu Ni,
  • Ashley Song,
  • Yanhui Su,
  • Hui Xue,
  • Amanda Yin

摘要

Let \(S_{\kappa }\) S κ be the space of cusp forms of weight \(\kappa \) κ and level one, and let \(S_{\kappa }^{*}\) S κ ∗ denote its dual space. In this paper, we find explicit spanning subsets of \(S_{\kappa }\) S κ consisting of Rankin-Cohen brackets of Eisenstein series and explicit subsets of periods that span \(S_{\kappa }^{*}\) S κ ∗ .