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  • The arithmetic of the values of modular functions and the divisors of modular forms

  • Jan H. Bruinier, Winfried Kohnen, Ken Ono
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 3 / May 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 552-566
    Print publication:
    May 2004
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  • We investigate the arithmetic and combinatorial significance of the values of the polynomials jn(x) defined by the q-expansion \[\sum_{n=0}^{\infty}j_n(x)q^n:=\frac{E_4(z)^2E_6(z)}{\Delta(z)}\cdot\frac{1}{j(z)-x}.\] They allow us to provide an explicit description of the action of the Ramanujan Theta-operator on modular forms. There are a substantial number of consequences for this result. We obtain recursive formulas for coefficients of modular forms, formulas for the infinite product exponents of modular forms, and new p-adic class number formulas.