Computations of Green’s function and its Fourier coefficients on Fuchsian groups. (English) Zbl 1267.11061

Avelin, Helen

Exp. Math. 19, No. 3, 317-334 (2010).

Summary: We develop algorithms for computations of Green’s function and its Fourier coefficients, \(F_n(z;s)\), on Fuchsian groups with one cusp. An analogue of a Rankin-Selberg bound for \(F_n(z;s)\) is presented.

MSC:

11F72	Spectral theory; trace formulas (e.g., that of Selberg)
11F30	Fourier coefficients of automorphic forms
33C10	Bessel and Airy functions, cylinder functions, \({}_0F_1\)

Keywords:

Green’s function; resolvent kernel; Rankin-Selberg bound; computational number theory; Fourier coefficients; algorithms; spectral theory; K-Bessel function; I-Bessel function

Software:

Algorithm 831

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