On the zeros of certain Poincaré series for $Γ_0^*(2)$ and $Γ_0^*(3)$

Details On the zeros of certain Poincaré series for $Γ_0^*(2)$ and $Γ_0^*(3)$ On the zeros of certain Poincaré series for $Γ_0^*(2)$ and $Γ_0^*(3)$

2006-12-21

arxiv.org/abs/math/0612631v3

Osaka J. Math. 47 (2010), 487--505

Mathematics

Number Theory

12 pages. http://www2.math.kyushu-u.ac.jp/~j.shigezumi/

Scientific paper

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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