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Fourier expansion at inequivalent cusps

Discussion in 'Mathematics' started by Gabriele, Oct 8, 2018.

  1. Gabriele

    Gabriele Guest

    Let $\Gamma\subset SL(2,\mathbb{R})$ be a Fuchsian group of the first kind. Let $c_1, c_2$ be inequivalent cusps of $\Gamma.$ Consider $f\in M_k(\Gamma)$ a weight $k$ holomorphic automorphic form, and suppose the Fourier expansion of $f$ at the cusp $c_1$ is known.

    Given the above expansion, is there an algorithm to compute (even numerically) the Fourier expansion of $f$ at the cusp $c_2$? Thanks!

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