On the Growth of the Taylor Coefficients of Automorphic Forms

Thomas A. Metzger
1973 Proceedings of the American Mathematical Society  
The growth of the Taylor coefficients of an automorphic form of dimension -2 with respect to a Fuchsian group T is related to the area integral Jfjj \F\s(\ -\z\%)'dxdy, and it is found that these coefficients must grow faster than a power of«. Moreover if Fe H(p, T) then these coefficients must grow slower than a different power of n and, in fact, an\n is square summable if either p=2 or 1<oo and T is finitely generated of the second kind.
doi:10.2307/2039640 fatcat:qjkg5i6aejgvvceclrnnoq3wve