Applications of a Pre–trace Formula to Estimates on Maass Cusp Forms
نویسنده
چکیده
By using spectral expansions in global automorphic Levi–Sobolev spaces, we estimate an average of the first Fourier coefficients of Maass cusp forms for SL2(Z), producing a soft estimate on the first numerical Fourier coefficients of Maass cusp forms, which is an example of a general technique for estimates on compact periods via application of a pre–trace formula. Incidentally, this shows that the distribution that evaluates the first Fourier coefficient of a Maass cusp form at height y > 1 lies in −1/2− ε global automorphic Levi–Sobolev space for every ε > 0. Moreover, we briefly explain the utility of Levi–Sobolev spaces and other modern analysis in the spectral theory of automorphic forms.
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