A trace formula for finite upper half planes
نویسنده
چکیده
In this paper, we prove a trace formula for finite upper half planes Hq. A brief outline is as follows: Fix a subgroup Γ ⊂ GL(2, Fq). The adjacency operators Aa act on functions in L(Γ\Hq); thus, we may consider Aa = Aa|L2(Γ\Hq). We prove a trace formula which is an equality between a weighted sum of the traces of the operators Aa and a sum over the conjugacy classes of Γ. The trace formula allows us to compute the trace of Aa . We compute the trace formula for the subgroups Γ = N and Γ = K of GL(2, Fq). 2000 Mathematics Subject Classification: Primary 11T60; Secondary 11F72.
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