Interlacing of zeros of the Eisenstein series for $\varGamma_0^+(2)$

We prove that for $a=2,4$, if $k\geq 16$ is an even integer, then the non-trivial zeros of $E_{k}^+$ and $E_{k+a}^+$ for $\Gamma_0^+(2)$ interlace on the arc of the fundamental domain for the Fricke group $\Gamma_0^+(2)$ of level $2$, where $E_{k}^+(z)$ i

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Publication Details

Journal
Acta Arithmetica
Published
2025-01-01
DOI
https://doi.org/10.4064/aa240304-15-1
Primary Topic
Advanced Algebra and Geometry
Type
article
Field-Weighted Citation Impact
0.00

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article

Interlacing of zeros of the Eisenstein series for $\varGamma_0^+(2)$

Bo‐Hae Im, Soyoung Choi
Acta Arithmetica
Advanced Algebra and Geometry
article

Interlacing of zeros of the Eisenstein series for $\varGamma_0^+(2)$

Bo‐Hae Im, Soyoung Choi
article en

Abstract

We prove that for $a=2,4$, if $k\geq 16$ is an even integer, then the non-trivial zeros of $E_{k}^+$ and $E_{k+a}^+$ for $\Gamma_0^+(2)$ interlace on the arc of the fundamental domain for the Fricke group $\Gamma_0^+(2)$ of level $2$, where $E_{k}^+(z)$ i

Acta ArithmeticaVol. 218(3)
Gyeongsang National University (KR), Department of Mathematical Sciences (RU)
National Research Foundation, National Research Foundation of Korea, Ministry of Science and ICT, South Korea
Openalex Percentile: Top 88%
Advanced Algebra and Geometry
DOIOpen Access PDFOpenAlex
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Interlacing of zeros of the Eisenstein series for $\varGamma_0^+(2)$ — Bo‐Hae Im, Soyoung Choi · Acta Arithmetica (2025) | TGRS Research Map | TGRS