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Asymptotic relations among Fourier coefficients of real-analytic Eisenstein series |
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| Authors: | Alvaro Alvarez-Parrilla |
| Institution: | Department of Mathematics, University of Maryland at College Park, College Park, Maryland 20740 |
| Abstract: | Following Wolpert, we find a set of asymptotic relations among the Fourier coefficients of real-analytic Eisenstein series. The relations are found by evaluating the integral of the product of an Eisenstein series As applications we find sets of asymptotic relations for divisor functions. |
| Keywords: | Automorphic forms Eisenstein series microlocal analysis divisor functions |
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with an exponential factor along a horocycle. We evaluate the integral in two ways by exploiting the automorphicity of 
; the first of these evaluations immediately gives us one coefficient, while the other evaluation provides us with a sum of Fourier coefficients. The second evaluation of the integral is done using stationary phase asymptotics in the parameter 
is the eigenvalue of 
) for a cubic phase.