Computations of Green's Function and Its Fourier Coefficients on Fuchsian Groups
Computations of Green's Function and Its Fourier Coefficients on Fuchsian Groups
Abstract We develop algorithms for computations of Green's function and its Fourier coefficients, Fn (z; s), on Fuchsian groups with one cusp. An analogue of a Rankin-Selberg bound for Fn (z; s) is presented. Keywords: Green's functionresolvent kernelRankin-Selberg boundcomputational number theoryFourier coefficientsalgorithmsspectral theory K-Bessel function I-Bessel function