On the zeros of Eisenstein series for $Γ_0^* (5)$ and $Γ_0^* (7)$

Details On the zeros of Eisenstein series for $Γ_0^* (5)$ and $Γ_0^* (7)$ On the zeros of Eisenstein series for $Γ_0^* (5)$ and $Γ_0^* (7)$

2006-07-18

arxiv.org/abs/math/0607409v2

Kyushu. J. Math. 61(2007), 527-549.

Mathematics

Number Theory

15 pages. http://www.math.kyushu-u.ac.jp/~j.shigezumi/

Scientific paper

10.2206/kyushujm.61.527

We locate almost all 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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