Abstract
To any finite symmetric subsetR ⊂ O3 corresponds a Hecke operatorTR on L2(S2) which leaves the eigenspaces ℋn (n ≥ 0) of the Laplacian invariant. We compute the trace ofTR | ℋn and prove that the sum of the positive eigenvalues ofTR on ⊕k=0n-1ℋk prevails over the modulus of the sum of the negative eigenvalues. For anym ∈ ℕ the integral quaternions of normm define such a Hecke operator\(T_{R_m } \), and renormalizing the traces ofTRm | ℋn slightly, we obtain sequences of Fourier coefficients of modular forms on Γ0(4).
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More From: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
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