On the zeros of Eisenstein series for Γ*0(2) and Γ*0(3)

Tsuyoshi Miezaki; Hiroshi Nozaki; Junichi Shigezumi

doi:10.2969/jmsj/05930693

On the zeros of Eisenstein series for Γ₀(2) and Γ₀(3)

Tsuyoshi Miezaki^*, Hiroshi Nozaki, Junichi Shigezumi

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

25 Citations (Scopus)

Abstract

We locate all of the zeros of the Eisenstein series associated with the Fricke groups Γ*₀(2) and Γ*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).

Original language	English
Pages (from-to)	693-706
Number of pages	14
Journal	Journal of the Mathematical Society of Japan
Volume	59
Issue number	3
DOIs	https://doi.org/10.2969/jmsj/05930693
Publication status	Published - 2007 Jul
Externally published	Yes

Keywords

Eisenstein series
Fricke group
Locating zeros
Modular forms

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.2969/jmsj/05930693

Cite this

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abstract = "We locate all of the zeros of the Eisenstein series associated with the Fricke groups Γ*0(2) and Γ*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).",

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author = "Tsuyoshi Miezaki and Hiroshi Nozaki and Junichi Shigezumi",

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AU - Miezaki, Tsuyoshi

AU - Nozaki, Hiroshi

AU - Shigezumi, Junichi

PY - 2007/7

Y1 - 2007/7

N2 - We locate all of the zeros of the Eisenstein series associated with the Fricke groups Γ*0(2) and Γ*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).

AB - We locate all of the zeros of the Eisenstein series associated with the Fricke groups Γ*0(2) and Γ*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).

KW - Eisenstein series

KW - Fricke group

KW - Locating zeros

KW - Modular forms

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