A detailed note on the zeros of Eisenstein series for $Γ_0^* (5)$ and $Γ_0^* (7)$

Details A detailed note on the zeros of Eisenstein series for $Γ_0^* (5)$ and $Γ_0^* (7)$ A detailed note on the zeros of Eisenstein series for $Γ_0^* (5)$ and $Γ_0^* (7)$

2006-07-11

arxiv.org/abs/math/0607247v4

Mathematics

Number Theory

39 pages, 3 Postscript figures. http://www2.math.kyushu-u.ac.jp/~j.shigezumi/

Scientific paper

The present paper provides the details omitted from the more concise study "On the zeros of Eisenstein series for $\Gamma_0^* (5)$ and $\Gamma_0^* (7)$." We locate almost all of the zeros of the Eisenstein series associated with the Fricke groups of level 5 and 7 in their fundamental domains by applying and extending the method of F. K. C. Rankin and H. P. F. Swinnerton-Dyer (1970). We also use the arguments of some terms of the Eisenstein series in order to improve existing error bounds.

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