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<p>The notion of double depth associated with quasi-Jacobi forms allows distinguishing, within the algebra <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{JS}^{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>JS</mtext> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation> of quasi-Jacobi singular forms of index zero, certain significant subalgebras (modular-type forms, elliptic-type forms, Jacobi forms). We study the stability of these subalgebras under the derivations of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textrm{JS}^{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>JS</mtext> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation> and through certain sequences of bidifferential operators constituting analogs of Rankin–Cohen brackets or transvectants.</p>

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Algèbres différentielles de formes quasi-Jacobi d’indice nul

  • 期刊论文

  • 发表日期：

    2026年4月21日

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  • François Dumas,
  • François Martin,
  • Emmanuel Royer

摘要

The notion of double depth associated with quasi-Jacobi forms allows distinguishing, within the algebra \(\textrm{JS}^{\infty }\) JS ∞ of quasi-Jacobi singular forms of index zero, certain significant subalgebras (modular-type forms, elliptic-type forms, Jacobi forms). We study the stability of these subalgebras under the derivations of \(\textrm{JS}^{\infty }\) JS ∞ and through certain sequences of bidifferential operators constituting analogs of Rankin–Cohen brackets or transvectants.