June 1, 1980Open Access

On the non-vanishing of Poincaré series

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Abstract

Let M = SL (2, Z) be the classical modular matrix group. One form of the Poincaré series on M is here z ∈ H =z = x + iy: y >0, q ≧ 2 and m ≧ 1 are integers, and the summation is over a complete system of matrices (ab: cd) in M with different lower row. The problem of the identical vanishing of the Poincaré series for different values of m and q goes back to Poincaré.

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Joseph Lehner (Sun,) studied this question.

synapsesocial.com/papers/69d814a95c3030ff03d192f4 https://doi.org/https://doi.org/10.1017/s0013091500003102

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