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A Note on Hecke's absolute Invariants
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Let Jq be Hecke's absolute invariant. The n-th Fourier coefficient of Jq is written in the form αq(n)r where αq(n) ∈ Q, rq∈ R. We regard αq(n) as a rational function of q. In § 3, it is proved that αq(n) is divisible by q2-4 for n > 2. This implies the conjecture of J. Raleigh [4]. Prime divisors of the denominator of αq (n) are also treated in § 4. In the last section, we propose interesting conjectures concerning αq (n).
Keywords
Hecke Group, J Function, Schwarzian Derivative.
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