Zeros of the combination of the Eisenstein series for Γ0+(2)

For even integers k ≥ ℓ ≥ 4 , we consider the modular forms E k + E ℓ + + E k + ℓ + for the Fricke group Γ 0 + ( 2 ) , where E k + is the Eisenstein series of weight k for Γ 0 + ( 2 ) , and we prove that if 26630 ≤ ℓ < k ≤ 77 ℓ or k = ℓ ≥ 10 , then all of their zeros in the fundamental domain  F...

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Bibliographic Details
Published in:The Ramanujan journal 2024-06, Vol.64 (2), p.475-488
Main Authors: Choi, SoYoung, Im, Bo-Hae
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
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Summary:For even integers k ≥ ℓ ≥ 4 , we consider the modular forms E k + E ℓ + + E k + ℓ + for the Fricke group Γ 0 + ( 2 ) , where E k + is the Eisenstein series of weight k for Γ 0 + ( 2 ) , and we prove that if 26630 ≤ ℓ < k ≤ 77 ℓ or k = ℓ ≥ 10 , then all of their zeros in the fundamental domain  F + for Γ 0 + ( 2 ) lie on the arc boundary of F + .
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-024-00836-3