A STIELTJES SEPARATION PROPERTY OF ZEROS OF EISENSTEIN SERIES

William FRENDREISS; Jennifer GAO; Austin LEI; Amy WOODALL; Hui XUE; Daozhou ZHU

doi:10.2206/kyushujm.76.407

Kyushu Journal of Mathematics

Online ISSN : 1883-2032
Print ISSN : 1340-6116
ISSN-L : 1340-6116

A STIELTJES SEPARATION PROPERTY OF ZEROS OF EISENSTEIN SERIES

William FRENDREISS, Jennifer GAO, Austin LEI, Amy WOODALL, Hui XUE, Daozhou ZHU

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Keywords: Eisenstein series, zeros of modular forms, separation property of zeros, divisibility between eigenforms

JOURNAL FREE ACCESS

2022 Volume 76 Issue 2 Pages 407-439

DOI https://doi.org/10.2206/kyushujm.76.407

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Abstract

For k < ℓ, let E_k(z) and E_ℓ(z) be Eisenstein series of weights k and ℓ, respectively, for SL₂(ℤ). We prove that between any two zeros of E_k(eⁱ^θ) there is a zero of E_ℓ(eⁱ^θ) on the interval π/2 < θ < 2π/3.

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