On the growth of the Taylor coefficients of automorphic forms
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- by Thomas A. Metzger PDF
- Proc. Amer. Math. Soc. 39 (1973), 321-328 Request permission
Abstract:
The growth of the Taylor coefficients of an automorphic form of dimension -2 with respect to a Fuchsian group $\Gamma$ is related to the area integral $\smallint {\smallint _U}|F{|^s}{(1 - |z{|^2})^t}dxdy$, and it is found that these coefficients must grow faster than a power of $n$. Moreover if $F \in H(p,\Gamma )$ then these coefficients must grow slower than a different power of $n$ and, in fact, ${a_n}/n$ is square summable if either $p = 2$ or $1 < p < \infty$ and $\Gamma$ is finitely generated of the second kind.References
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Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 39 (1973), 321-328
- MSC: Primary 10D15
- DOI: https://doi.org/10.1090/S0002-9939-1973-0313193-5
- MathSciNet review: 0313193