ON 2-ADIC MODULAR FORMS ON 2-ADIC MODULAR FORMS

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Author(s)

Abstract

Let f(τ) be a Hauptmodul for Γ_0(2) that has zero at the cusp infinity. We construct the 2-adic modular form f^^~ from f(τ) by using Atkin's method, which is an eigenfunction of the Hecke operator U. We expand f^^~ as a formal power series in f(τ). We can compute explicitly the 2-adic ordinal of these coefficients of the f-expansion of f^^~. We show that f^^~ coincides with the 2-adic modular form constructed from the modular invariant j(τ) by using Atkin's method.

Let ƒ(τ) be a Hauptmodul for Γ<SUB>0</SUB>(2) that has zero at the cusp infinity. We construct the 2-adic modular form ƒ from ƒ(τ) by using Atkin’s method, which is an eigenfunction of the Hecke operator <I>U</I> . We expand ƒ as a formal power series in ƒ(τ). We can compute explicitly the 2-adic ordinal of these coefficients of the ƒ -expansion of ƒ. We show that ƒ coincides with the 2-adic modular form constructed from the modular invariant <I>j</I>(τ) by using Atkin’s method.

Journal

  • Kyushu Journal of Mathematics

    Kyushu Journal of Mathematics 64(2), 199-214, 2010

    Faculty of Mathematics, Kyushu University

Codes

  • NII Article ID (NAID)
    130000441856
  • NII NACSIS-CAT ID (NCID)
    AA10994346
  • Text Lang
    ENG
  • Article Type
    Departmental Bulletin Paper
  • ISSN
    1340-6116
  • Data Source
    IR  J-STAGE 
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