Conformal maps and critical points of Eisenstein series

2025/06/26 by Mario Bonk, Bonk, Mario · 1 citation
Mathematics · #11F11 #30C20 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2506.21471

openalex publication_date 2025/06/26 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

We investigate the critical points of the basic (quasi-)modular forms E₂, E₄, and E₆. They occur where some associated polymorphic functions have poles. By an explicit description of these polymorphic functions as conformal maps, one can give an accurate qualitative analysis of the locations of the critical points of E₂, E₄, and E₆.

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