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

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 5 October 2007

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1191591853

Digital Object Identifier
doi:10.2969/jmsj/05930693

Mathematical Reviews number (MathSciNet)
MR2344823

Zentralblatt MATH identifier
1171.11024

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

Keywords
Eisenstein series Fricke group locating zeros modular forms

Citation

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. https://projecteuclid.org/euclid.jmsj/1191591853.


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References

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