Location and double interlacing of zeros of certain combination of the Eisenstein series for Γ0+(2)

We show that the zeros of aE2k+(z)−(Ek+(z))2 and bE2k+(z)+(Ek+(z))2 lie on the arc of the fundamental domain for the Fricke group Γ0+(2) of level 2, where Ek+(z) is the Eisenstein series for Γ0+(2), and we investigate the doubly interlacing property between non-elliptic zeros of aE2k+(z)−(Ek+(z))2 a...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 537; no. 2
Main Authors Choi, SoYoung, Im, Bo-Hae
Format Journal Article
LanguageEnglish
Published Elsevier Inc 15.09.2024
Subjects
Eisenstein series
Fricke group
Hecke group
Eisenstein series
Hecke group
Fricke group
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Summary:We show that the zeros of aE2k+(z)−(Ek+(z))2 and bE2k+(z)+(Ek+(z))2 lie on the arc of the fundamental domain for the Fricke group Γ0+(2) of level 2, where Ek+(z) is the Eisenstein series for Γ0+(2), and we investigate the doubly interlacing property between non-elliptic zeros of aE2k+(z)−(Ek+(z))2 and bE2k+(z)+(Ek+(z))2.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2024.128397