Journal of the Mathematical Society of Japan

On the zeros of Eisenstein series for $\mathbf{\Gamma_0^{*}(2)}$ and $\mathbf{\Gamma_0^{*}(3)}$

Tsuyoshi MIEZAKI, Hiroshi NOZAKI, and Junichi SHIGEZUMI

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

Article information

J. Math. Soc. Japan Volume 59, Number 3 (2007), 693-706.

First available in Project Euclid: 5 October 2007

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Zentralblatt MATH identifier

Primary: 11F11: Holomorphic modular forms of integral weight
Secondary: 11F12: Automorphic forms, one variable

Eisenstein series Fricke group locating zeros modular forms


MIEZAKI, Tsuyoshi; NOZAKI, Hiroshi; SHIGEZUMI, Junichi. On the zeros of Eisenstein series for $\mathbf{\Gamma_0^{*}(2)}$ and $\mathbf{\Gamma_0^{*}(3)}$. J. Math. Soc. Japan 59 (2007), no. 3, 693--706. doi:10.2969/jmsj/05930693.

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