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<p>We study the structure of the vector space of Drinfeld quasi-modular forms for congruence subgroups. We provide representations as polynomials in the false Eisenstein series with coefficients in the space of Drinfeld modular forms (the <i>E</i>-expansion), and, whenever possible, as sums of hyperderivatives of Drinfeld modular forms. Moreover, we introduce and study the double-slash operator, and use it to provide a well-posed definition for Hecke operators on Drinfeld quasi-modular forms. We characterize eigenforms and, for the special case of Hecke congruence subgroups <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\Gamma _0(\mathfrak {m})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="normal">Γ</mi> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="fraktur">m</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>, we give explicit formulas for the Hecke action on <i>E</i>-expansions.</p>

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Drinfeld quasi-modular forms of higher level

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月25日

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  • Andrea Bandini,
  • Maria Valentino,
  • Sjoerd de Vries

摘要

We study the structure of the vector space of Drinfeld quasi-modular forms for congruence subgroups. We provide representations as polynomials in the false Eisenstein series with coefficients in the space of Drinfeld modular forms (the E-expansion), and, whenever possible, as sums of hyperderivatives of Drinfeld modular forms. Moreover, we introduce and study the double-slash operator, and use it to provide a well-posed definition for Hecke operators on Drinfeld quasi-modular forms. We characterize eigenforms and, for the special case of Hecke congruence subgroups \(\Gamma _0(\mathfrak {m})\) Γ 0 ( m ) , we give explicit formulas for the Hecke action on E-expansions.