On the zeros of certain Poincar\'e series for $\Gamma_0^*(2)$ and $\Gamma_0^*(3)$

Junichi Shigezumi

arxiv: math/0612631 · v3 · submitted 2006-12-21 · 🧮 math.NT

On the zeros of certain Poincar\'e series for Gamma₀^(2) and Gamma₀^(3)

Junichi Shigezumi This is my paper

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keywords gammaserieszeroscertainapplyingassociateddomainseisenstein

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We locate all of the zeros of certain Poincare series associated with the Fricke groups $\Gamma_0^*(2)$ and $\Gamma_0^*(3)$ in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (``On the zeros of Eisenstein series'', 1970).

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On the zeros of certain Poincar\'e series for Gamma₀^*(2) and Gamma₀^*(3)

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On the zeros of certain Poincar\'e series for Gamma₀^(2) and Gamma₀^(3)