Applications of Spectral Theory of Automorphic Forms
نویسنده
چکیده
on Γ\H, parametrized as λw = w(w−1). Haas listed the w-values. Haas thought he was solving the differential equation (∆ − λ)u = 0. Stark and Hejhal observed zeros of ζ and of an L-function on Haas’ list. This suggested an approach to proving the Riemann Hypothesis, since it seemed that zeros w of ζ might give eigenvalues λ = w(w − 1) of ∆. Since ∆ is a self-adjoint, nonpositive operator, these eigenvalues would necessarily be nonpositive, forcing either Re(w) = 2 or w ∈ [0, 1]. Hejhal attempted to reproduce Haas’ results with more careful computations, but the zeros failed to appear on Hejhal’s list!
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